Rotation sets of billiards flows

Zainab Abdullah Alsheekhhussain

    Research output: ThesisDoctoral Thesis

    60 Downloads (Pure)

    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 languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • The University of Western Australia
    Award date31 Oct 2017
    DOIs
    Publication statusUnpublished - 2017

    Fingerprint

    Billiards
    Periodic Trajectories
    Strictly Convex
    Convex Body
    Euclidean space
    Torus

    Cite this

    Alsheekhhussain, Zainab Abdullah. / Rotation sets of billiards flows. 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.",
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    school = "The University of Western Australia",

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    Alsheekhhussain, ZA 2017, 'Rotation sets of billiards flows', Doctor of Philosophy, The University of Western Australia. https://doi.org/10.4225/23/5a051c2a279b0

    Rotation sets of billiards flows. / Alsheekhhussain, Zainab Abdullah.

    2017.

    Research output: ThesisDoctoral Thesis

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    T1 - Rotation sets of billiards flows

    AU - Alsheekhhussain, Zainab Abdullah

    PY - 2017

    Y1 - 2017

    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

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