Ergodic Theory and Dynamical Systems



Ergodic attractors as limits of hyperbolic horseshoes


FERNANDO JOSÉ SÁNCHEZ-SALAS a1
a1 Departamento de Matematicas y Computacion, Facultad de Ciencias, Universidad del Zulia, Venezuela (e-mail: fsanchez@luz.ve)

Abstract

Let f:M\rightarrow M be a C^2 diffeomorphism of a compact Riemannian manifold of dimension m\geq 2 leaving invariant an ergodic Sinai–Ruelle–Bowen measure \mu with non-zero Lyapunov exponents. We prove that \mu can be approximated by ergodic measures supported on hyperbolic horseshoes with arbitrarily large unstable dimensions.

(Received August 8 1999)
(Revised March 8 2001)