Properties of the maximal entropy measure and geometry of Hénon attractors

Details Properties of the maximal entropy measure and geometry of Hénon attractors Properties of the maximal entropy measure and geometry of Hénon attractors

2012-02-13

arxiv.org/abs/1202.2822v1

Mathematics

Dynamical Systems

53 pages, 5 figures

Scientific paper

We show the existence and uniqueness of the maximal entropy measure for non-uniformly hyperbolic $C^2$-H\'enon like diffeomorphisms. This follows mostly from a geometrical study of the attractor and a conjugacy of a subset with a strongly positive recurrent Markov shift. Moreover a coding of the periodic points shows that the maximal entropy measure is equidistributed on them. The maximal entropy measure is also shown to be finitarily Bernoulli, exponentially mixing and satisfying the central limit Theorem.

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