Uniform hyperbolic approximations of measures with non zero Lyapunov exponents

Details Uniform hyperbolic approximations of measures with non zero Lyapunov exponents Uniform hyperbolic approximations of measures with non zero Lyapunov exponents

2011-08-22

arxiv.org/abs/1108.4334v2

Mathematics

Dynamical Systems

11 pages, improved introduction and additional background and references. To appear in Proc. AMS

Scientific paper

We show that for any C^1+alpha diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that there exists a sequence Omega_n of compact, topologically transitive, locally maximal, uniformly hyperbolic sets, such that for any sequence mu_n of f-invariant ergodic probability measures with supp (mu_n) in Omega_n we have mu_n -> mu in the weak-* topology.

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