Past Seminars- Dynamical Systems

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  • Victor Kleptsyn
    Fri Nov 2, 2018
    2:00 pm
    We consider random products of SL(2, R) matrices that depend on a parameter in a non-uniformly hyperbolic regime. We show that if the dependence on the parameter is monotone then almost surely the random product has upper (limsup) Lyapunov exponent that is equal to the value prescribed by the Furstenberg Theorem (and hence positive) for all...
  • Victor Kleptsyn
    Tue Oct 30, 2018
    1:00 pm
        The classical Polya urn process is a reinforcement process, in which there are balls of different color in the urn, we take out a ball at random, and the color that was just out of it gets an advantage for all future turns: we return this ball to the urn and add another one of the same color.     ...
  • D.Burago
    Thu Oct 25, 2018
    2:00 pm
     Three different math stories in one lecture. Only definitions, motivations, results, some ideas behind proofs, open questions.  1. One of the greatest achievements in Dynamics in the XX century is the KAM Theory. It says that a small perturbation of a non-degenerate completely integrable system still has an overwhelming...
  • Wes Whiting
    Tue Apr 24, 2018
    1:00 pm
    Hyperbolic-type metrics extend the idea of negative curvature to metric spaces, and several well-behaved hyperbolic-type metrics are known on 1-punctured Euclidean space. However, they lose their hyperbolicity on spaces with non-singleton boundary. In this talk, I will discuss the obstructions to hyperbolicity on more general boundaries, and give...
  • Victor Kleptsyn
    Tue Mar 13, 2018
    1:00 pm
    The study of the equation on the 2-torus given by   x’= sin x + a + b sin t has been motivated by its relation to the Josephson junction in physics, as well as by purely mathematical reasons. For any values of the parameters a and b, one can consider the time-2\pi (period) map from the x-circle to itself, and study...
  • Victor Kleptsyn
    Tue Mar 6, 2018
    1:00 pm
    The talk will be devoted to the study of finitely generated groups acting on the circle. We will start with joint results with A. Navas and B. Deroin: if such an action by analytic diffeomorphisms admits a Cantor minimal set, then this set is of Lebesgue measure zero, and if such an action by free group of analytic...
  • Anton Gorodetski
    Tue Nov 14, 2017
    1:00 pm
    We will discuss several open problems in dynamical systems (related to random dynamical systems with parameters, sums of Cantor sets, etc.) that can potentially turn into a research project suitable for graduate students.