Dynamical Systems Seminar

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Statistical Properties of Some Mostly Expanding Fast-Slow Partially Hyperbolic Systems

Speaker: Jacopo De Simoi, University of Toronto

Location: Warren Weaver Hall 312

Date: Thursday, December 5, 2024, 4:30 p.m.

Synopsis:

Abstract: In this joint work with K. Fernando and N. Fleming-Vázquez, we consider a class of sufficiently smooth two-dimensional fast-slow partially hyperbolic systems. This class is obtained by perturbing a trivial extension of a one-parameter family of one-dimensional expanding maps.  We assume that the averaged system has exactly one sink and that both Lyapunov exponents of the system are positive.  Using an elaboration on the technique of standard pairs, we will show that, for sufficiently small perturbations, there exists a unique SRB measure for the system; we also show that the system exhibits exponential decay of correlations for Hölder observables with explicit, nearly optimal bounds.  This work is a "mostly expanding" counterpart of the analogous result for "mostly contracting" systems (i.e. with one negative Lyapunov exponent) which was studied in a joint work with C. Liverani several years ago.