Inverse pressure estimates and the independence of stable dimension for non-invertible maps

Details Inverse pressure estimates and the independence of stable dimension for non-invertible maps Inverse pressure estimates and the independence of stable dimension for non-invertible maps

2008-11-19

arxiv.org/abs/0811.3227v1

Canadian Journal of Mathematics, vol. 60, no.3, 2008, 658-684

Mathematics

Dynamical Systems

24 pages

Scientific paper

We use the inverse pressure concept to estimate the stable dimension for hyperbolic non-invertible maps which are conformal in the stable fibers. The non-invertible case is different than the diffeomorphism case. In particular we show that if the map is open on the respective basic set, then the stable dimension is constant everywhere. We prove also in this setting the Lipschitz continuity of the stable distribution.

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