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.

Committee Chair

Renato Feres

Committee Members

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

Comments

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

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2016

Language

English (en)

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Mathematics Commons

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