GT Théorie Ergodique et Systèmes Dynamiques
Lyapunov spectrum rigidity and simultaneous linearization of random Anosov diffeomorphisms
04
Nov. 2024
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Intervenant : Yi Shi
Institution : Sichuan University
Heure : 10h15 - 11h45
Lieu : IMO, Salle 2L8

Let f be a Cr Anosov diffeomorphism on T2 and {f1,...,fk} be a family of Cr-random perturbations of f with r>2. We show that if the positive Lyapunov exponent of any stationary SRB measure of {f1,...,fk} is equal to the positive Lyapunov exponent of linearization A in GL(2,Z) of f, then the stable foliation of {f1,...,fk} are non-random and Cr-smooth.

If we further assume the negative Lyapunov exponent of the stationary SRB measure also equals A, then there exists a smooth conjugacy h on T2, such that h o fi o h-1 = A+vi for every i=1,...,k. The same result holds for random perturbations of generic hyperbolic automorphism A in GL(d,Z).

This is a joint work with A. Brown.

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