Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle

Details Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle

1996-04-22

arxiv.org/abs/math/9604238v1

Mathematics

Dynamical Systems

Scientific paper

We prove the existence of Sinai-Ruelle-Bowen measures for a class of $C^2$ self-mappings of a rectangle with unbounded derivatives. The results can be regarded as a generalization of a well-known one dimensional Folklore Theorem on the existence of absolutely continuous invariant measures. In an earlier paper analogous results were stated and the proofs were sketched for the case of invertible systems. Here we give complete proofs in the more general case of noninvertible systems, and, in particular, develop the theory of stable and unstable manifolds for maps with unbounded derivatives.

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