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BEGIN:VEVENT
SUMMARY:Jeroen Lamb (Imperial College London)
DTSTART:20201123T150000Z
DTEND:20201123T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/1
DESCRIPTION:Title: Bifurcation in the presence of noise\nby Jeroen Lamb (Imperial C
ollege London) as part of UAB dynamical systems group international semina
r\n\n\nAbstract\nWe discuss some recent progress in the development of a\n
bifurcation theory for random dynamical systems\, touching upon\nthe follo
wing publications:\n\n- Maximilian Engel\, Jeroen S. W. Lamb\, and Martin
Rasmussen\, Bifurcation\nanalysis of a stochastically driven limit cycle\,
Communications in\nMathematical Physics 365\, 3 (2019)\, 935−942.\n\n-
Maximilian Engel\, Jeroen S. W. Lamb\, and Martin Rasmussen\, Conditioned\
nLyapunov exponents for random dynamical systems\, Transactions of the\nAm
erican Mathematical Society 372\, 9 (2019)\, 6343−6370.\n\n- Thai Son Do
an\, Maximilian Engel\, Jeroen S. W. Lamb\, and Martin\nRasmussen\, Hopf b
ifurcation with additive noise\, Nonlinearity 31\, 10\n(2018)\, 4567−460
1.\n\n- Mark Callaway\, Thai Son Doan\, Jeroen S. W. Lamb\, and Martin Ras
mussen\,\nThe dichotomy spectrum for random dynamical systems and pitchfor
k\nbifurcations with additive noise\, Annales de l'Institut Henri Poincar
é\nProbabilités et Statistiques 53\, 4 (2017)\, 1548−1574.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Villari (Università degli Studi di Firenze)
DTSTART:20201130T150000Z
DTEND:20201130T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/2
DESCRIPTION:Title: Recent contributions and some open questions in the qualitative beha
viour of certain generalized Liénard equations\nby Gabriele Villari (
Università degli Studi di Firenze) as part of UAB dynamical systems group
international seminar\n\n\nAbstract\nThe aim of this talk is to present s
ome recent results\, together with some\nopen questions\, concerning the p
hase-portrait of certain generalized Liénard\nequations.\nAt frst I will
briefly discuss some joint work with Jean Mawhin\, Fabio Zanolin and Timot
eo Carletti for the relativistic Liénard equation\n$$\n\\frac{d}{dx}\\fra
c{\\dot{x}}{\\sqrt{1-x^2}}+f(x)\\dot{x}+g(x)=0\n$$\nas well as for the cas
e with prescrived curvature\n$$\n\\frac{d}{dx}\\frac{\\dot{x}}{\\sqrt{1-x^
2}}+\\lambda{}f(x)\\dot{x}+g(x)=0\n$$\nIn this framework\, a generalizatio
n in wich a function $f (x\,\\dot{x})$ takes the role\nof the function $f
(x)$ will be also presented.\nHowever\, the main part of the talk will con
centrate on a very recent joint\nresult with Fabio Zanolin\, concerning th
e generalized Liénard system\n$$\n\\dot{x} = y − F (x\, y)\\\\\n\\dot{y
} = −g(x)\n$$\nand focusing on the case in which\n$F (x\, y) = \\lambda{
}B(y)A(x)$\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josep Maria Cors (Universitat Politècnica de Catalunya)
DTSTART:20201214T150000Z
DTEND:20201214T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/3
DESCRIPTION:Title: A tour around Central Configurations\nby Josep Maria Cors (Unive
rsitat Politècnica de Catalunya) as part of UAB dynamical systems group i
nternational seminar\n\n\nAbstract\nIn Celestial Mechanics a configuration
of the $N$-body problem is\ncentral if the acceleration vector for each b
ody is a common scalar\nmultiple of its position vector (with respect to t
he center of mass).\nThe aim of the talk is to visit some of the recently
studied problems:\n$1+n$\, Co-circular\, Crowns\, Stacked five body-proble
m\, Convex four\nbody-problem\, ... to get the feeling of the topic.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (Instituto de Ciencias Matemáticas)
DTSTART:20201221T150000Z
DTEND:20201221T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/4
DESCRIPTION:Title: New results on the dynamics of the steady Euler flows\nby Daniel
Peralta-Salas (Instituto de Ciencias Matemáticas) as part of UAB dynamic
al systems group international seminar\n\n\nAbstract\nA volume-preserving
vector field $X$ on a manifold $M$ is Eulerisable if there exists a Rieman
nian metric $g$ on $M$ such that $X$ satisfies the stationary Euler equati
ons on $(M\,g)$. In this talk I will review some recent results on the dyn
amics of Eulerisable flows. In the first part I will present a homological
characterization which generalizes the classical one by Sullivan for geod
esible flows\; as an application\, I will show that this result implies th
at the Eulerisable flows cannot exhibit (volume-preserving) plugs. This is
based on joint work with Ana Rechtman and Francisco Torres de Lizaur. In
the second part\, I will show that the Eulerisable flows are universal in
the sense of Tao\, i.e.\, any non-autonomous dynamics is extendable to an
Euler flow on a sphere of sufficiently high dimension for some Riemannian
metric. This implies\, in particular\, the Turing completeness of the Eule
r fields. This is based on joint work with Robert Cardona\, Eva Miranda an
d Francisco Presas.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Rademacher (Universität Bremen)
DTSTART:20210111T150000Z
DTEND:20210111T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/5
DESCRIPTION:Title: Pulse replication and accumulation of eigenvalues\nby Jens Radem
acher (Universität Bremen) as part of UAB dynamical systems group interna
tional seminar\n\n\nAbstract\nThis talk concerns the spatial dynamics appr
oach to dynamical phenomena in partial differential equations (PDE) posed
on the real line. Motivated by pulse-replication phenomena observed in the
FitzHugh--Nagumo equation\, traveling pulses whose slow-fast profiles exh
ibit canard-like transitions are investigated. It is shown that the spectr
a of the PDE linearization about such pulses may contain many point eigenv
alues that accumulate onto a union of curves as the slow scale parameter a
pproaches zero. The limit sets are related to the absolute spectrum of the
homogeneous rest states involved in the canard-like transitions.\nThis is
joint work with Paul Carter (Minneapolis) and Bjorn Sandstede (Providence
)\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Panazzolo (Université de Haute-Alsace)
DTSTART:20210118T150000Z
DTEND:20210118T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/6
DESCRIPTION:Title: Versal regularization of vector fields with cross type discontinuiti
es.\nby Daniel Panazzolo (Université de Haute-Alsace) as part of UAB
dynamical systems group international seminar\n\n\nAbstract\nI will expose
some aspects of the regularization of vector fields with discontinuities
along non-smooth sets. The basic problem in the background is to develop a
theory of versal regularisations\, which captures all possible dynamics
resulting from changing the regularization method.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tere M. Seara (Universitat Politècnica de Catalunya)
DTSTART:20210125T150000Z
DTEND:20210125T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/7
DESCRIPTION:Title: Non existence of small amplitude breathers for the reversible Klein-
Gordon equation\nby Tere M. Seara (Universitat Politècnica de Catalun
ya) as part of UAB dynamical systems group international seminar\n\n\nAbst
ract\nBreathers are periodic in time spatially localized solutions of evol
utionary PDEs. They are known to exist for the sine-Gordon equation but ar
e believed to be rare in other Klein-Gordon equations. Exchanging the role
s of time and position\, breathers can be interpreted as homoclinic soluti
ons to a steady solution.\n\nIn this talk\, I will explain how to show tha
t\, under generic asumptions\, the Klein-Gordon equation does not have bre
athers whose amplitude is smaller than a certain quantity. The key point i
s to obtain an asymptotic formula for the distance between the stable and
unstable manifold of the steady solution when the steady solution has weak
ly hyperbolic one dimensional stable and unstable manifolds. Their distanc
e is exponentially small with respect to the amplitude of the breather and
therefore classical perturbative techniques cannot be applied.\n\nThis is
a joint work with O. Gomide (Universidade Federal de Goiás)\, M. Guardia
(U. Politecnica de Catalunya) and C. Zeng (Georgiatech I.)\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Douglas Duarte Novaes (Universidade Estadual de Campinas)
DTSTART:20210201T150000Z
DTEND:20210201T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/8
DESCRIPTION:Title: Sliding Shilnikov dynamics in non-smooth systems and applications.\nby Douglas Duarte Novaes (Universidade Estadual de Campinas) as part o
f UAB dynamical systems group international seminar\n\n\nAbstract\nIn the
theory of piecewise smooth vector fields a Sliding Shilnikov Orbit is a tr
ajectory\, in the\nFilippov sense\, connecting a saddle focus pseudo-equil
ibrium to itself. Recently\, it has been shown\nthat this connection provi
des a chaotic dynamic without further assumptions. \nIn this talk\, we exp
lore the dynamics of this connection and an application for biological mod
els is presented.\n\n\nReferences:\n\nD.D. Novaes\, G. Ponce\, and R. Var
ão\, Chaos induced by sliding phenomena in Filippov systems\, J. Dyn. Dif
f. Equat. 29 (2017)\, 1569-1583.\n\nD.D.Novaes and M. A. Teixeira\, Shilni
kov problem in nonsmooth dynamical systems\, Chaos 29\, 063110 (2019).\n\n
T. Carvalho\, D.D. Novaes\, and L.F. Gonçalves\, Sliding Shilnikov Connec
tion in Filippov-type Predator-Prey Model\, Nonlinear Dynamics\, 100(3)\,
2973-2987.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chara Pantazi (Universitat Politècnica de Catalunya)
DTSTART:20210208T150000Z
DTEND:20210208T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/9
DESCRIPTION:Title: Integrability and linearizability for some families of three dimensi
onal quadratic systems\nby Chara Pantazi (Universitat Politècnica de
Catalunya) as part of UAB dynamical systems group international seminar\n\
n\nAbstract\nThis talk concerns the problem of local integrability at the
origin of some families in three dimensions. First I present some results
about the local integrability at the origin of a nine parametric family of
a three dimensional Lotka--Volterra differential systems with 3:-1:2-reso
nance. More concrete I present the necessary and sufficient conditions on
the parameters of the family that guarantee the existence of two independ
ent local first integrals at the origin of coordinates. Additionally\, I p
resent the cases where the origin is linearizable. Then\, I present a stu
dy of another nine parametric family of quadratic systems with 1:-2:1 res
onance at the origin and the axes planes do not need to be invariant. For
some subfamily I present the conditions that guarantee the non-existence
of a polynomial first integral.\n\nThe first part of the talk is a joint w
ork with W. Aziz(Salahaddin University-Erbil\, Iraq)\, C. Christopher(Plym
outh University\, UK) and J. Llibre(UAB\, Catalonia\,Spain). The second pa
rt of the talk is a joint work with W. Aziz(Salahaddin University-Erbil\,
Iraq) and A. Amen(Salahaddin University-Erbil\, Iraq).\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Luis Bravo (Universidad de Extremadura)
DTSTART:20210222T150000Z
DTEND:20210222T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/10
DESCRIPTION:Title: Generating non-trivial limit cycles in Abel equations\nby José
Luis Bravo (Universidad de Extremadura) as part of UAB dynamical systems
group international seminar\n\n\nAbstract\nLet us fix trigonometric monomi
als $A_k$ and integers $n_k\\geq 1$\, $k=1\,\\ldots\,m$\, and\nconsider th
e family of Abel-like differential equations\n$$x'=\\sum_{k=1}^m a_k A_k(t
) x^{n_k}\,$$ where $a_k\\in\\mathbb{R}$.\n\nThis equation always has the
trivial solution $x(t)\\equiv 0$. Moreover\,\neither every bounded solutio
n is $2\\pi$-periodic or $2\\pi$-periodic solutions\nare isolated. In the
first case\, we say that the equation has a center\nand in the second case
\, we call limit cycle to any $2\\pi$-periodic solution.\n\nWe are interes
ted in studying whether there exist equations\nof the family with non-triv
ial limit cycles. That is\, if there exist $a_1\,\\ldots\,a_m$\nsuch that
the differential equation has a limit cycle different from $x(t)=0$.\n\nWe
will focus on the special case $\\{n_k\\colon k=1\,\\ldots m\\}=\\{n_1\,n
_2\\}$\, $n_1\,n_2\\geq 2$ and $n_1\\neq n_2$.\nIn this case\, we will ``a
lmost'' determine all the families having equations with non-trivial\nlimi
t cycles. This ``almost'' is due to a special family in which we have not
been able to determine\nwhether there exist or not non-trivial limit cycle
s\, though we suspect the existence of non-trivial limit cycles.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilei Tang (Shanghai Jaio Tong University)
DTSTART:20210301T150000Z
DTEND:20210301T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/11
DESCRIPTION:Title: Some results of limit cycles in Lienard systems and applications\nby Yilei Tang (Shanghai Jaio Tong University) as part of UAB dynamical
systems group international seminar\n\n\nAbstract\nThe aim of this talk is
to present our some recent results of limit cycles in planar smooth and p
iecewise smooth Lienard differential systems\, including existence\, uniqu
eness\, stability and hyperbolicity of limit cycles.\nMoreover\, using the
se results for the limit cycles together with other qualitative methods an
d techniques\, we can obtain the exact number of limit cycles and further
obtain the global dynamics and bifurcations in some biological and mechani
cal models.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Muldowney (University of Alberta)
DTSTART:20210308T150000Z
DTEND:20210308T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/12
DESCRIPTION:Title: Bendixson Conditions for Differential Equations in a Banach Space\nby James Muldowney (University of Alberta) as part of UAB dynamical sy
stems group international seminar\n\n\nAbstract\nA Bendixson Condition pre
cludes the invariance of Jordan curves with respect to the dynamics of a d
ifferential equation $x’ = f(x)$. Thus\, for example\, non-constant peri
odic orbits and homoclinic cycles are ruled out. As we know\, for 2-dimens
ional systems if div f is non-zero in a simply connected open set U in the
plane\, we know that there are no periodic orbits in U. We will explore s
uch conditions in various finite and infinite dimensional spaces.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Walcher (RWTH Aachen)
DTSTART:20210315T150000Z
DTEND:20210315T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/13
DESCRIPTION:Title: Characteristic curves of (quasi-)homogeneous vector fields\nby
Sebastian Walcher (RWTH Aachen) as part of UAB dynamical systems group int
ernational seminar\n\n\nAbstract\nCharacteristic curves of homogeneous vec
tor fields have in recent years experienced a kind of renaissance\, due to
interest in "eigenvectors of tensors" from various applications. In the s
eminar talk we relate the general concept for quasi-homogeneous vector fie
lds to symmetry properties\, and present and extend some existence results
. Moreover an application to finding degree bounds for semi-invariants of
polynomial vector fields will be discussed\, as well as an application to
determining the structure of the centralizer of a local analytic or formal
vector field.\nThe talk reports on recent joint work with G. Gaeta\, N. K
ruff\, J. Llibre\, C. Pantazi and X. Zhang (in various combinations).\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Martí Pete (University of Liberpool)
DTSTART:20210215T150000Z
DTEND:20210215T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/14
DESCRIPTION:Title: On the computability of Julia sets in the exponential family\nb
y David Martí Pete (University of Liberpool) as part of UAB dynamical sys
tems group international seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adriana Buică (Universitatea Babeș-Bolyai Cluj-Napoca)
DTSTART:20210322T150000Z
DTEND:20210322T160000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/15
DESCRIPTION:Title: Ulam-Hyers stability and exponentially dichotomic evolution equatio
ns in Banach spaces\nby Adriana Buică (Universitatea Babeș-Bolyai Cl
uj-Napoca) as part of UAB dynamical systems group international seminar\n\
n\nAbstract\nIn 1941 D. Hyers gave an answer to the following question of
S. Ulam. "Suppose that f satisfies only approximately the equation $f(x+y)
=f(x)+f(y)$. Then does there exist a solution of this equation which f app
roximates?" Since then\, this type of stability was studied for functional
equations\, difference equations\, and differential equations\, too. The
first notable result for differential equations is that $x'=\\lambda{}x$ i
s Ulam-Hyers\nstable on $\\mathbb{R}$ if and only if $\\lambda\\neq0$. In
this talk we prove that the system $X'=AX$ is Ulam-Hyers stable on $\\mat
hbb{R}$ if and only if $A$ is hyperbolic. We generalize this result for ev
olution\nfamilies in Banach spaces using results from the book Evolution S
emigroups in Dynamical Systems and Differential Equations by C. Chicone an
d Y. Latushkin. The stability is maintained when adding a nonlinear term w
hich is globally Lipschitz and whose Lipschitz constant is sufficiently sm
all.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Mawhin (Université Catholique de Louvain)
DTSTART:20210426T140000Z
DTEND:20210426T150000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/16
DESCRIPTION:Title: Zeros and surjectivity of continuous mappings in $R^n$\nby Jean
Mawhin (Université Catholique de Louvain) as part of UAB dynamical syste
ms group international seminar\n\n\nAbstract\nIn this lecture\, we use Bro
uwer degree to obtain in a simple way a number of results on the existence
of zeros and the surjectivity of continuous nonlinear mappings in $n$-di
mensional Euclidian space.\n\nThe results generalize and unify a number of
classical ones\, like the Hadamard and the Poincaré-Miranda theorem\, an
d some of them make use of possibly discontinuous auxiliary mappings and o
f convexity techniques.\n\nMost of them can be extended to some special cl
asses of mappings in Banach spaces.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiang Zhang (Shanghai Jiao Tong University)
DTSTART:20210412T140000Z
DTEND:20210412T150000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/17
DESCRIPTION:Title: Jacobian conjecture in $\\mathbb{R}^2$\nby Xiang Zhang (Shangha
i Jiao Tong University) as part of UAB dynamical systems group internation
al seminar\n\n\nAbstract\nIn this talk we introduce our solution to Jacobi
an conjecture in $\\mathbb{R}^2$. The main tools are from qualitative theo
ry of dynamical systems.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Bonckaert (Hasselt University)
DTSTART:20210503T140000Z
DTEND:20210503T150000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/18
DESCRIPTION:Title: Planar saddle points and formal Gevrey series\nby Patrick Bonck
aert (Hasselt University) as part of UAB dynamical systems group internati
onal seminar\n\n\nAbstract\nPlanar vector fields $X$ near a saddle type $p
:-p$ resonant singular point are considered. The use of Ecalle-Roussarie l
og-like compensators in linearizing conjugacies is carried out\, and Gevr
ey-type estimates are presented. Attention is given to the unfolding of th
e resonance with one parameter.\n\nIn the analytic case an approximative n
ormal form with a flat remainder of an explicit type is described\, includ
ing parameter dependence\, also in the (formally linearizable) non-resonan
t case.\n\nFinally\, we indicate some questions in the non-resonant case\,
about the possible use of compensators related to the rational approximan
ts.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulij S. Ilyashenko (National Research University Higher School of
Economics\, Moscow)
DTSTART:20210531T130000Z
DTEND:20210531T140000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/19
DESCRIPTION:Title: Large bifurcation supports\nby Yulij S. Ilyashenko (National Re
search University Higher School of Economics\, Moscow) as part of UAB dyna
mical systems group international seminar\n\n\nAbstract\nGlobal bifurcatio
n theory on the sphere is now in the study of its creation. The subject of
the talk is: given a degenerate vector field\, determine\, what part of i
ts phase portrait actually bifurcates? The talk is devoted to an answer to
this question obtained in a joint work with Natalya Goncharuk. This answe
r is expected to be a powerful tool in the study of classification and str
uctural stability of generic families of vector fields on the sphere with
an arbitrary number of parameters.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Liz (Universidade de Vigo)
DTSTART:20210510T140000Z
DTEND:20210510T150000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/20
DESCRIPTION:Title: Four bifurcations and a global stability result in a family of dela
y differential equations\nby Eduardo Liz (Universidade de Vigo) as par
t of UAB dynamical systems group international seminar\n\n\nAbstract\nIn t
his lecture\, we introduce a family of delay-differential equations with m
any applications in various fields such as economics\, population dynamics
and physiological systems.\nWe present some new results on the global dyn
amics of this equation\, focusing on a particular but representative examp
le. Bifurcation diagrams using relevant model parameters show some intere
sting features\, such as stability switches and extinction windows due to
sudden collapses.\nFor the general case\, we also state and outline the pr
oof of a sharp delay-independent global stability result\, showing that it
works for our main examples. The interplay between the continuous dynami
cal system generated by the delay equation and an associated one-dimensio
nal discrete dynamical system plays an essential role in our approach.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Geyer (TU Delft)
DTSTART:20210517T140000Z
DTEND:20210517T150000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/21
DESCRIPTION:Title: Stability and persistence of periodic traveling waves\nby Anna
Geyer (TU Delft) as part of UAB dynamical systems group international semi
nar\n\n\nAbstract\nIn the first part of my talk\, I will present a result
on the stability of smooth periodic traveling waves of the Camassa-Holm eq
uation. This equation models the propagation of shallow water waves and ha
s been studied extensively. The problem of spectral stability of periodic
waves however was still open. The key to obtaining the spectral stability
is that the periodic waves can be characterised by an alternative Hamilton
ian structure\, different from the standard formulation.\n\nIn the second
part of my talk\, I will focus on the problem of persistence of periodic t
raveling waves in Hamiltonian PDE (for instance\, the Camassa-Holm equatio
n) under perturbations. I will show that the number of traveling waves th
at persist are controlled by the zeros of certain Abelian integrals. Moreo
ver we will see that one can design the perturbations precisely so that an
y prescribed number of traveling waves persists.\n\nThe first part is join
t work with Dmitry Pelinovsky and Fabio Natali\, the second part with Arme
ngol Gasull and Víctor Mañosa\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaume Llibre (Universitat Autònoma de Barcelona)
DTSTART:20210531T100000Z
DTEND:20210531T110000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/22
DESCRIPTION:Title: Results and open problems on the algebraic limit cycles of the plan
ar polynomial differential systems\nby Jaume Llibre (Universitat Autò
noma de Barcelona) as part of UAB dynamical systems group international se
minar\n\n\nAbstract\nIn this talk we summarize some results and open probl
ems on the algebraic limit cycles of the planar polynomial differential sy
stems. More precisely\,\n\n 1.- we study the maximum number of algebrai
c limit cycles of the polynomial differential differential systems of degr
ee n\;\n\n 2.- we show how to use the algebraic limit cycles for provin
g that any finite configuration of limit cycles can be realized by some po
lynomial differential system\;\n\n 3.- we provide the maximum number of
algebraic limit cycles formed by circles that a polynomial differential s
ystem of degree $n$ can exhibit\;\n\n 4.- we study the algebraic limit
cycles of the polynomial differential systems of degree 2.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Misiurewicz (Purdue University Indianapolis)
DTSTART:20210531T141000Z
DTEND:20210531T151000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/23
DESCRIPTION:Title: Flexibility of entropies for piecewise expanding unimodal maps\
nby Michal Misiurewicz (Purdue University Indianapolis) as part of UAB dyn
amical systems group international seminar\n\n\nAbstract\nWe investigate t
he flexibility of the entropy (topological and metric) for the class of pi
ecewise expanding unimodal maps. We show that the only restrictions for th
e values of the topological and metric entropies in this class are that bo
th are positive\, the topological entropy is at most log 2\, and the metri
c entropy is not larger than the topological entropy. In order to have a b
etter control on the metric entropy\, we work mainly with topologically mi
xing piecewise expanding skew tent maps\, for which there are only 2 diffe
rent slopes. For those maps\, there is an additional restriction that the
topological entropy is larger than (1/2) log 2. Moreover\, we generalize a
nd give a different interpretation of the Milnor-Thurston formula connecti
ng the topological entropy and the kneading determinant for unimodal maps.
\nThis is joint work with Lluís Alsedà and Rodrigo Pérez.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dierk Schleicher (Institut de Mathématiques de Marseille)
DTSTART:20210419T133000Z
DTEND:20210419T143000Z
DTSTAMP:20260422T212924Z
UID:SeminarGSDUAB/24
DESCRIPTION:Title: Finding polynomial roots using complex analysis\, dynamical systems
\, computer algebra\nby Dierk Schleicher (Institut de Mathématiques d
e Marseille) as part of UAB dynamical systems group international seminar\
n\n\nAbstract\nOne of the classical problems in all areas of mathematics i
s to find roots of complex polynomials. It is well known that this can be
done only by methods of approximation. We discuss three classical methods:
the Newton\, Weierstrass\, and Ehrlich-Aberth methods\; these are complex
analytic maps that\, under iteration\, are supposed to converge to one ro
ot\, resp. all roots of the polynomial. Locally\, these methods converge f
ast\, but the global dynamical properties are hard to describe.\nWe introd
uce these complex analytic dynamical systems and describe recent progress
towards their global dynamical properties. In particular\, the Newton and
Weierstrass methods are not globally convergent: for open sets of polynomi
als there are open sets of initial points that fail to converge to roots.
Moreover\, for Weierstrass and Ehrlich-Aberth\, there are orbits that are
always defined and converge\, but not to roots. For Newton\, there is mean
while a rich theory about its global dynamics\, but there are many open qu
estions for all these methods.\nMuch of this is joint work with members of
my ERC team\, in particular my PhD student Bernhard Reinke (who will pres
ent more details on Thursday)\, as well as with colleagues.\n
LOCATION:https://researchseminars.org/talk/SeminarGSDUAB/24/
END:VEVENT
END:VCALENDAR