Polynomial decay of correlations for generalized baker’s transformations via anisotropic Banach spaces methods and operator renewal theory

Date

2016-05-02

Authors

Chart, Seth William

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Abstract

We apply anisotropic Banach space methods together with operator renewal theory to obtain polynomial rates of decay of correlations for a class of generalized baker's transformations. The polynomial rates were proved for a smaller class of observables in a 2013 paper of Bose and Murray by fundamentally different methods. Our approach provides a direct analysis of the Frobenius-Perron operator associated to a generalized baker's transformation in contrast to the paper of Bose and Murray where decay rates are obtained for a factor map and lifted to the full map.

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Keywords

Smooth Ergodic Theory, Decay of Correlations, Generalized Baker's Transformations, Dynamical Systems

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