Date of Award

9-2013

Document 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 hy- perbolic dynamical systems. We examine cases in which polynomial decay of cor- relations leads to a CLT with a non-standard scaling factor of p n ln n. We also formulate an explicit expression for the the di ffusion constant o 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.

Included in

Mathematics Commons

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