Date of Award

Spring 5-15-2016

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Doctor of Philosophy (PhD)

Degree Type

Dissertation

Abstract

We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. A general theory of rigid body collisions in is developed, which returns the known dimension two model as a special case but generalizes to higher dimensions. We give new results on periodicity and boundedness of orbits which suggest that a class of billiards (including all polygons) is not ergodic. Computer generated phase portraits demonstrate non-ergodic features, suggesting chaotic no-slip billiards cannot easily be constructed using the common techniques for generating chaos in standard billiards. However, Sinai type dispersing billiards, which are always ergodic in the case of standard billiards, appear to be ergodic above a certain curvature threshold.

Language

English (en)

Chair and Committee

Renato Feres

Committee Members

Tim Chumley, John McCarthy, Xiang Tang, Mladen V. Wickerhauser,

Comments

Permanent URL: https://doi.org/10.7936/K747484H

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