BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Chiara Caracciolo (Università degli Studi di Roma "Tor Vergata")
DTSTART;VALUE=DATE-TIME:20200511T081500Z
DTEND;VALUE=DATE-TIME:20200511T100000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/1
DESCRIPTION:Title: Elliptic tori in FPU chains\nby Chiara Caracciolo (Università
degli Studi di Roma "Tor Vergata") as part of Dynamical Systems and Compu
tations\n\n\nAbstract\nWe revisit an algorithm constructing elliptic tori
via normal form\, that was originally\n designed to apply to planetary pro
blems. The scheme is adapted to properly work with models of chains of N +
1 particles interacting via anharmonic potentials\, thus covering also th
e case of FPU lattices. We successfully apply our new algorithm to the con
struction of 1-dimensional elliptic tori for wide sets of the parameter (i
.e.\, the total energy of the system) that rules the size of the perturbat
ion in FPU chains with N = 4\, 8. Moreover\, we show the stability of the
regions surrounding the 1-dimensional elliptic tori. Finally\, we compare
our semi-analytical results with those provided by numerical explorations
of the FPU-model dynamics\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Philipe Lessard (McGill University)
DTSTART;VALUE=DATE-TIME:20200603T140000Z
DTEND;VALUE=DATE-TIME:20200603T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/2
DESCRIPTION:Title: Rigorous integration of infinite dimensional dynamical systems via
Chebyshev series\nby Jean-Philipe Lessard (McGill University) as part
of Dynamical Systems and Computations\n\n\nAbstract\nIn this talk we intr
oduce recent general methods to rigorously \n\n\ncompute solutions of infi
nite dimensional Cauchy problems. The idea \n\n\nis to expand the solution
s in time using Chebyshev series \n\n\nand use the contraction mapping the
orem to construct a neighbourhood \n\n\nabout an approximate solution whic
h contains the exact solution of the \n\n\nCauchy problem. We apply the me
thods to some semi-linear parabolic partial \n\n\ndifferential equations (
PDEs) and delay differential equations (DDEs).\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Estevez (Universidade Federal do Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20200528T131500Z
DTEND;VALUE=DATE-TIME:20200528T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/3
DESCRIPTION:Title: Some recent results on multicritical circle maps\nby Gabriela
Estevez (Universidade Federal do Rio de Janeiro) as part of Dynamical Syst
ems and Computations\n\n\nAbstract\nWe study circle maps with a finite num
ber of "inflexive" critical points\, the called multicritical circle maps.
The topology of these maps is well understood. One of the main questions
in one dimensional dynamics is on the conditions that make the topology de
termines the geometry. In this talk\, we will discuss some recent results
concerning this question for these circle maps.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Capinski (AGH)
DTSTART;VALUE=DATE-TIME:20200616T131500Z
DTEND;VALUE=DATE-TIME:20200616T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/4
DESCRIPTION:Title: Arnold Diffusion and Stochastic Behaviour\nby Maciej Capinski
(AGH) as part of Dynamical Systems and Computations\n\n\nAbstract\nWe will
discuss a construction of a stochastic process on energy levels in pertur
bed Hamiltonian systems. The method follows from shadowing of dynamics of
two coupled horseshoes. It leads to a family of stochastic processes\, whi
ch converge to a Brownian motion with drift\, as the perturbation paramete
r converges to zero. Moreover\, we can obtain any desired values of the dr
ift and variance for the limiting Brownian motion\, for appropriate sets o
f initial conditions. The convergence is in the sense of the functional ce
ntral limit theorem. We give an example of such construction in the PRE3BP
.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igors Gorbovickis (Jacobs University Bremen)
DTSTART;VALUE=DATE-TIME:20201014T121500Z
DTEND;VALUE=DATE-TIME:20201014T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/5
DESCRIPTION:Title: Critical points of the multipliers in the quadratic family: equidi
stribution and accumulation\nby Igors Gorbovickis (Jacobs University B
remen) as part of Dynamical Systems and Computations\n\n\nAbstract\nA para
meter $c_0\\in\\mathbb C$ in the family of quadratic polynomials $f_c(z)=z
^2+c$ is a \\textit{critical point of a period $n$ multiplier}\, if the ma
p $f_{c_0}$ has a periodic orbit of period $n$\, whose multiplier\, viewed
as a locally analytic function of $c$\, has a vanishing derivative at $c=
c_0$. \nInformation about the location of critical points and critical val
ues of the multipliers might play a role in the study of the geometry of t
he Mandelbrot set. \n\nWe will discuss asymptotic behavior of critical poi
nts of the period $n$ multipliers as $n\\to\\infty$. We will show that whi
le the critical points equidistribute on the boundary of the Mandelbrot se
t $\\mathbb M$\, their accumulation set $\\mathcal X$ is strictly larger t
han $\\partial\\mathbb M$. \n\nIn order to study the geometry of the accum
ulation set $\\mathcal X$\, we will introduce a new family of sets $\\math
cal Y_c$ that relate to $\\mathcal X$ in a somewhat similar way as the fil
led Julia sets relate to the Mandelbrot set.\n\n\nWe will further show tha
t the accumulation set $\\mathcal X$ is bounded\, path connected and conta
ins the Mandelbrot set as a proper subset. This is joint work with Tanya F
irsova.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonguk Yang (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20201105T124500Z
DTEND;VALUE=DATE-TIME:20201105T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/6
DESCRIPTION:Title: Polynomials with a Siegel disk of Bounded Type\nby Jonguk Yang
(Stony Brook University) as part of Dynamical Systems and Computations\n\
n\nAbstract\nConsider a polynomial with a rotational domain (called a Sieg
el disc) of bounded type rotation number. It is known that the Siegel boun
dary is a quasi-circle that contains at least one critical point. In the q
uadratic case\, this means that the entire post-critical set is trapped wi
thin the Siegel boundary\, where the theory of real analytic circle maps p
rovides us with excellent control. However\, in the higher degree case\, t
here exist multiple critical points. A priori\, these “free” critical
points may accumulate on the Siegel boundary in a complicated way\, causin
g extreme distortions in the geometry nearby. In my talk\, I show that in
fact\, this does not happen\, and that the dynamics of the polynomial can
be fully understood near the Siegel boundary.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Wolf (City College of New York)
DTSTART;VALUE=DATE-TIME:20201120T141500Z
DTEND;VALUE=DATE-TIME:20201120T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/7
DESCRIPTION:Title: Computability of topological pressure on compact shift spaces be
yond finite type\nby Christian Wolf (City College of New York) as part
of Dynamical Systems and Computations\n\n\nAbstract\nIn this talk we disc
uss the computability (in the sense of computable analysis) of the topolog
ical pressure P_T(phi) on compact shift spaces X for continuous potentials
phi: X -> R. This question has recently been studied for subshifts of fin
ite type (SFTs) and their factors (Sofic shifts). We develop a framework t
o address the computability of the topological pressure on general shift s
paces and apply this framework to coded shifts. In particular\, we prove t
he computability of the topological pressure for all continuous potentials
on S-gap shifts\, generalized gap shifts\, and Beta shifts. We also const
ruct shift spaces which\, depending on the potential\, exhibit computabili
ty and non-computability of the topological pressure. We further show that
the generalized pressure function (X\,phi) |-> P_T(X\,phi|_X) is not comp
utable for a large set of shift spaces X and potentials phi. Along the way
of developing these computability results\, we derive several ergodic-the
oretical properties of coded shifts which are of independent interest beyo
nd the realm of computability. The topic of the talk is joint work with Mi
chael Burr (Clemson U.)\, Shuddho Das (NYU) and Yun Yang (Virginia Tech).\
n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Mireles James (Florida Atlantic University)
DTSTART;VALUE=DATE-TIME:20201211T141500Z
DTEND;VALUE=DATE-TIME:20201211T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/8
DESCRIPTION:Title: Validated Numerics for Morse Indices of Delay Differential Equatio
ns\nby Jason Mireles James (Florida Atlantic University) as part of Dy
namical Systems and Computations\n\n\nAbstract\nI will review a little bit
some basic ideas about delay differential equations (DDEs)\, in particula
r that they generate discrete time dynamical systems on an appropriate fun
ction space. Then I'll talk about the problem of obtaining a mathematicall
y rigorous count on the number of unstable eigenvalues at an equilibrium s
olution (the Morse index). The eigenvalues of a DDE solve a transcendental
characteristic equation\, so that a lower bound on the Morse index is obt
ained by proving the existence of solutions of this nonlinear equation in
the open right half of the complex plane. A more delicate question is\, ho
w do know when we have found all the solutions? How do we know when to sto
p? This is counting problem and I will talk about a couple of different po
ssible solutions\, including one based on Chebyshev spectral methods. This
is joint work with J.P. Lessard.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Rodrigues (Universidade do Porto)
DTSTART;VALUE=DATE-TIME:20210129T121500Z
DTEND;VALUE=DATE-TIME:20210129T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/9
DESCRIPTION:Title: Unfolding a Bykov attractor: from an attracting torus to strange a
ttractors\nby Alexandre Rodrigues (Universidade do Porto) as part of D
ynamical Systems and Computations\n\n\nAbstract\nIn this talk\, we present
a mechanism for the emergence of strange attractors in a two-parametric f
amily of differential equations acting on a three-dimensional sphere. When
both parameters are zero\, its flow exhibits an attracting heteroclinic n
etwork (Bykov attractor) made by two 1-dimensional and one 2-dimensional s
eparatrices between two hyperbolic saddles-foci with different Morse indic
es.\n\nAfter slightly increasing both parameters\, while keeping the one-d
imensional connections unaltered\, we focus our attention in the case wher
e the two-dimensional invariant manifolds of the equilibria do not interse
ct. We show the existence of many complicated dynamical objects\, ranging
from an attracting quasi-periodic torus\, Newhouse sinks to Hénon-like st
range attractors\, as a consequence of the Torus Bifurcation Theory (devel
oped by Afraimovich and Shilnikov).\n\nUnder generic and checkable hypothe
ses\, we conclude that any analytic unfolding of a Hopf-zero singularity (
within an appropriate class) contains strange attractors. We also discuss
the case of the existence of rank-one strange attractors (developed by Q.
Wang and L.-S. Young) for this model.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanya Firsova (Kansas State University)
DTSTART;VALUE=DATE-TIME:20210416T131500Z
DTEND;VALUE=DATE-TIME:20210416T151500Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/10
DESCRIPTION:Title: Critical points of the multiplier map: equidistribution and accum
ulation\nby Tanya Firsova (Kansas State University) as part of Dynamic
al Systems and Computations\n\n\nAbstract\nWe study asymptotic properties
of the critical points of the multiplier map. The multiplier of a non-para
bolic orbit of a map $z\\to z^2+c$ can be extended by means of analytic co
ntinuation to a multiple-valued algebraic function on the space of quadrat
ic polynomials $z^2+c$. We show that as the period of the periodic orbit i
ncreases to infinity\, critical points of the multiplier map equidistribut
e on the boundary of the Mandelbrot set. We also prove that the accumulati
on set of the critical points of multipliers is larger than the boundary o
f the Mandelbrot set. The accumulation set is a bounded path connected set
\, and it in fact contains all of the Mandelbrot set. This is a joint work
with I. Gorbovickis.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Remus Radu (Uppsala Universitet)
DTSTART;VALUE=DATE-TIME:20210510T131500Z
DTEND;VALUE=DATE-TIME:20210510T151500Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/11
DESCRIPTION:Title: Rigidity for complex Hénon maps\nby Remus Radu (Uppsala Univ
ersitet) as part of Dynamical Systems and Computations\n\n\nAbstract\nThe
forward escaping set of a dissipative complex Hénon map is a well-underst
ood dynamical object. By works of Hubbard & Oberste-Vorth it is biholomorp
hic to an universal object: $(C-\\bar{D})\\times C$ factored by a discrete
group of automorphisms isomorphic to $Z[1/2]/Z$. We use this analytic des
cription to show that two Hénon maps with biholomorphic escaping sets are
in fact the same. In her work Tanase extended this description of the esc
aping set to the boundary in order to capture the Julia set and introduced
a one-dimensional invariant set that encodes part of the dynamics of the
Hénon map. We show that this invariant is also a rigid object for the Hé
non map. This talk is based on joint work with Sylvain Bonnot and Raluca T
anase.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raluca Tanase (Uppsala Universitet)
DTSTART;VALUE=DATE-TIME:20210518T111500Z
DTEND;VALUE=DATE-TIME:20210518T131500Z
DTSTAMP;VALUE=DATE-TIME:20240328T192613Z
UID:CAPA_UU_SEMINAR/12
DESCRIPTION:Title: On hyperbolicity and partial hyperbolicity in the Hénon family
a>\nby Raluca Tanase (Uppsala Universitet) as part of Dynamical Systems an
d Computations\n\n\nAbstract\nWe discuss new regions of hyperbolicity and
partial hyperbolicity for the complex Hénon map and show where they sit i
n the parameter space in $C^2$.\n
LOCATION:https://researchseminars.org/talk/CAPA_UU_SEMINAR/12/
END:VEVENT
END:VCALENDAR