Uniform hyperbolic approximations of measures with non zero Lyapunov exponents
Abstract
We show that for any C1+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 Omegan of compact, topologically transitive, locally maximal, uniformly hyperbolic sets, such that for any sequence mun of f-invariant ergodic probability measures with supp (mun) in Omegan we have mun -> mu in the weak-* topology.
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