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Time-quantitative behavior of geodesics on the cube surface
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Yang, Yuxuan. Time-quantitative behavior of geodesics on the cube surface. Retrieved from https://doi.org/doi:10.7282/t3-sd7y-1p26

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TitleTime-quantitative behavior of geodesics on the cube surface
NameYang, Yuxuan (author); Beck, Jozsef (chair); Beck, Jozsef (member); Narayanan, Bhargav (member); Zeilberger, Doron (member); Chen, William Wai Lim (member); Rutgers University; School of Graduate Studies
Date Created2022
Other Date2022-05 (degree)
SubjectMathematics, Cube surface, Geodesic, Representation theory, Uniform distribution
Extent100 pages : illustrations
DescriptionThe cube surface is the simplest and perhaps most natural example of closed surface endowed with a flat metric with several cone-type singularities. We study the qualitative and quantitative behaviors of geodesics on this surface. We focus on uniformity(=equidistribution): given any ”nice” test set, when the length of a geodesic goes to infinity, is the proportion of the geodesic that lies in the test set close to the relative area of the test set? Ergodic theorists have given a qualitative theory of non-integrable flat dynamical systems. With our non-ergodic approaches, we give many time-quantitative results. In this paper, we introduce several powerful methods for this problem. One of the most interesting ideas is to use representation theory to utilize symmetry.
NotePh.D.
NoteIncludes bibliographical references
Genretheses
Persistent URLhttps://doi.org/doi:10.7282/t3-sd7y-1p26
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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