Date of Award
9-2013
Document type
dissertation
Access Type
Open Access Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Hongkun Zhang
Second Advisor
Luc Rey-Bellet
Third Advisor
Bruce Turkington
Subject Categories
Mathematics
Abstract
In this thesis we study the central limit theorem (CLT) for nonuniformly hyperbolic dynamical systems. We examine cases in which polynomial decay of correlations leads to a CLT with a non-standard scaling factor of √ n ln n. We also formulate an explicit expression for the the diffusion constant σ in situations where a return time function on the system is a certain class of supermartingale. We then demonstrate applications by exhibiting the CLT for the return time function in four classes of dynamical billiards, including one previously unproven case, the skewed stadium, as well as for the linked twist map. Finally, we introduce a new class of billiards which we conjecture are ergodic, and we provide numerical evidence to support that claim.
DOI
https://doi.org/10.7275/vd8y-jv94
Recommended Citation
Mohr, Luke, "Martingale Central Limit Theorem and Nonuniformly Hyperbolic Systems" (2013). Open Access Dissertations. 810.
https://doi.org/10.7275/vd8y-jv94
https://scholarworks.umass.edu/open_access_dissertations/810