Abstracts Mathematics

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

by Seth William Chart

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. Advisors/Committee Members: Bose, Christopher (supervisor).