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Ergodic attractors as limits of hyperbolic horseshoes

Published online by Cambridge University Press:  07 May 2002

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

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 2 , April 2002 , pp. 571 - 589
Copyright
2002 Cambridge University Press

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