Expansive measures versus Lyapunov exponents

Armijo, Alma; Pacifico, Maria

doi:10.1090/proc/14089

Expansive measures versus Lyapunov exponents
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by Alma Armijo and Maria José Pacifico PDF

Proc. Amer. Math. Soc. 146 (2018), 3895-3906 Request permission

Abstract:

In this paper we investigate the relation between measure-expansiveness and hyperbolicity. We prove that non-atomic invariant ergodic measures with all of their Lyapunov exponents positive are positively measure-expansive. We also prove that local diffeomorphisms robustly positively measure-expansive are expanding. Finally, we prove that a $C^1$-volume-preserving diffeomorphism that cannot be accumulated by positively measure-expansive diffeomorphisms has a dominated splitting.

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