Stability of Statistical Properties in Two-Dimensional Piecewise Hyperbolic Maps

Mark Demers; Carlangelo Liverani

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

Stability of Statistical Properties in Two-Dimensional Piecewise Hyperbolic Maps

Mark Demers, Carlangelo Liverani

Fairfield University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Transactions of the American Mathematical Society
Volume	360
DOIs	https://doi.org/10.1090/S0002-9947-08-04464-4
State	Published - Jan 1 2008

Disciplines

Computer Sciences
Physical Sciences and Mathematics

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10.1090/S0002-9947-08-04464-4License: CC BY

Stability of Statistical Properties in Two-Dimensional PiecewiseFinal published version, 511 KBLicense: CC BY

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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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AB - 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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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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Stability of Statistical Properties in Two-Dimensional Piecewise Hyperbolic Maps

Abstract

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