Stability of statistical properties in two-dimensional piecewise hyperbolic maps

Demers, Mark; Liverani, Carlangelo

doi:10.1090/S0002-9947-08-04464-4

Stability of statistical properties in two-dimensional piecewise hyperbolic maps
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by Mark F. Demers and Carlangelo Liverani PDF

Trans. Amer. Math. Soc. 360 (2008), 4777-4814

Abstract:

We investigate the statistical properties of a piecewise smooth dynamical system by directly studying the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional maps with uniformly bounded second derivative. For the class of systems at hand, we obtain a complete description of the SRB measures, their statistical properties and their stability with respect to many types of perturbations, including deterministic and random perturbations and holes.

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