Rotation sets of billiards flows

Zainab Abdullah Alsheekhhussain

doi:10.4225/23/5a051c2a279b0

Rotation sets of billiards flows

Zainab Abdullah Alsheekhhussain

Research output: Thesis › Doctoral Thesis

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Abstract

The thesis studies rotation sets for billiards flows in the exterior of several strictly convex bodies in Euclidean spaces (open billiards) and tori. In both cases, the thesis shows that the rotation set is convex, and the rotation vectors of periodic trajectories are dense in the rotation set. In addition, for open billiards with circular obstacles, it shows that the general rotation set can be obtained by an explicit, purely geometric construction.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Stoyanov, Luchezar, Supervisor Noakes, Lyle, Supervisor
Award date	31 Oct 2017
DOIs	https://doi.org/10.4225/23/5a051c2a279b0
Publication status	Unpublished - 2017

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10.4225/23/5a051c2a279b0

THESIS - DOCTOR OF PHILOSOPHY - ALSHEEKHHUSSAIN Zainab Abdullah - 2017
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title = "Rotation sets of billiards flows",

abstract = "The thesis studies rotation sets for billiards flows in the exterior of several strictly convex bodies in Euclidean spaces (open billiards) and tori. In both cases, the thesis shows that the rotation set is convex, and the rotation vectors of periodic trajectories are dense in the rotation set. In addition, for open billiards with circular obstacles, it shows that the general rotation set can be obtained by an explicit, purely geometric construction. ",

keywords = "rotation theory, rotation vectors, open billiards, periodic trajectories, general rotation set, torus, billiards on a torus",

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AU - Alsheekhhussain, Zainab Abdullah

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N2 - The thesis studies rotation sets for billiards flows in the exterior of several strictly convex bodies in Euclidean spaces (open billiards) and tori. In both cases, the thesis shows that the rotation set is convex, and the rotation vectors of periodic trajectories are dense in the rotation set. In addition, for open billiards with circular obstacles, it shows that the general rotation set can be obtained by an explicit, purely geometric construction.

AB - The thesis studies rotation sets for billiards flows in the exterior of several strictly convex bodies in Euclidean spaces (open billiards) and tori. In both cases, the thesis shows that the rotation set is convex, and the rotation vectors of periodic trajectories are dense in the rotation set. In addition, for open billiards with circular obstacles, it shows that the general rotation set can be obtained by an explicit, purely geometric construction.

KW - rotation theory

KW - rotation vectors

KW - open billiards

KW - periodic trajectories

KW - general rotation set

KW - torus

KW - billiards on a torus

U2 - 10.4225/23/5a051c2a279b0

DO - 10.4225/23/5a051c2a279b0

M3 - Doctoral Thesis

ER -

Rotation sets of billiards flows

Abstract

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