Physical measures at the boundary of hyperbolic maps

Details Physical measures at the boundary of hyperbolic maps Physical measures at the boundary of hyperbolic maps

2004-09-21

arxiv.org/abs/math/0409391v3

Discrete Contin. Dyn. Syst. 20 (2008), no. 4, 849--876.

Mathematics

Dynamical Systems

29 pages, 2 figures, 44 references. Minor corrections

Scientific paper

We consider diffeomorphisms of a compact manifold with a dominated splitting
which is hyperbolic except for a "small" subset of points (Hausdorff dimension
smaller than one, e.g. a denumerable subset) and prove the existence of
physical measures and their stochastical stability. The physical measures are
obtained as zero-noise limits which are shown to satisfy the Entropy Formula.

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