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(Fibrewise) Anosov Systems.pdf (1012.93 KB)

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(Fibrewise) Anosov Systems

Zhang, Danyu
http://rave.ohiolink.edu/etdc/view?acc_num=osu1681917323434056

Abstract Details

2023, Doctor of Philosophy, Ohio State University, Mathematics.
A fibrewise Anosov system (a diffeomorphism or a flow) is a system on a fibre bundle that preserves an invariant stable and unstable splitting along the fibres. In this thesis, we discuss a global rigidity result, that is, every fibrewise Anosov diffeomorphism on a principal torus bundle is topologically conjugate to a map that is linear in the fibres, which can be seen as a parametrized version of the Franks-Manning classification of Anosov diffeomorphisms on torus. We also include a chapter to discuss the classification problems of Anosov diffeomorphisms, and an appendix that exposits the Tomter's algebraic examples of Anosov flows, which are fibrewise Anosov flows.
Andrey Gogolev (Advisor)
Jean-François Lafont (Committee Member)
Michael Walter Davis (Committee Member)
Mathematics

Recommended Citations

Citations

  • Zhang, D. (2023). (Fibrewise) Anosov Systems [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1681917323434056

    APA Style (7th edition)

  • Zhang, Danyu. (Fibrewise) Anosov Systems. 2023. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1681917323434056.

    MLA Style (8th edition)

  • Zhang, Danyu. "(Fibrewise) Anosov Systems." Doctoral dissertation, Ohio State University, 2023. http://rave.ohiolink.edu/etdc/view?acc_num=osu1681917323434056

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.