Nonhyperbolicity of invariant measures on maximal attractor

Details Nonhyperbolicity of invariant measures on maximal attractor Nonhyperbolicity of invariant measures on maximal attractor

2008-07-30

arxiv.org/abs/0807.4963v1

Mathematics

Dynamical Systems

Scientific paper

The article states that for every compact manifold M of dimension 4 or higher there is an area U in a set of smooth diffeomorphisms over M such that every map f from U has local maximal partially hyperbolic attractor and nonatomic ergodic invariant measure on it where one of Lyapunov exponents vanish. The result is first proved for skew products over horseshoe and then transferred onto smooth diffeomorphisms.

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