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:20200511T081500Z DTEND:20200511T100000Z DTSTAMP:20260422T213012Z 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:20200603T140000Z DTEND:20200603T150000Z DTSTAMP:20260422T213012Z 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:20200528T131500Z DTEND:20200528T150000Z DTSTAMP:20260422T213012Z 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:20200616T131500Z DTEND:20200616T150000Z DTSTAMP:20260422T213012Z 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:20201014T121500Z DTEND:20201014T140000Z DTSTAMP:20260422T213012Z 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:20201105T124500Z DTEND:20201105T140000Z DTSTAMP:20260422T213012Z 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:20201120T141500Z DTEND:20201120T160000Z DTSTAMP:20260422T213012Z 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:20201211T141500Z DTEND:20201211T160000Z DTSTAMP:20260422T213012Z 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:20210129T121500Z DTEND:20210129T140000Z DTSTAMP:20260422T213012Z 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:20210416T131500Z DTEND:20210416T151500Z DTSTAMP:20260422T213012Z 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:20210510T131500Z DTEND:20210510T151500Z DTSTAMP:20260422T213012Z 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:20210518T111500Z DTEND:20210518T131500Z DTSTAMP:20260422T213012Z UID:CAPA_UU_SEMINAR/12 DESCRIPTION:Title: On hyperbolicity and partial hyperbolicity in the Hénon family\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