The approximation of Lyapunov exponents by horseshoes for $C^1$-diffeomorphisms with dominated splitting

Abstract

Let $f$ be a $C^1$-diffeomorphism and $\mu$ be a hyperbolic ergodic $f$-invariant Borel probability measure with positive measure-theoretic entropy. Assume that the Oseledec splitting $$T_{x}M=E_1(x)\oplus \cdots \oplus E_s(x)\oplus E_{s+1}(x)\oplus \cdots \oplus E_l(x)$$ is dominated on the Oseledec basin $\Gamma$. We give extensions of Katok's Horseshoes construction. Moreover there is a dominated splitting corresponding to Oseledec subspace on horseshoes.

References in corpus (1)

• $C^1$ density of stable ergodicity

Cited by in corpus (1)

• Horseshoes and Lyapunov exponents for Banach cocycles over nonuniformly hyperbolic systems