University of Illinois Urbana-Champaign

Dynamics of Symplectic Piecewise Affine Elliptic Rotation Maps on Tori

Kahng, Byungik

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Description

Title
Dynamics of Symplectic Piecewise Affine Elliptic Rotation Maps on Tori
Author(s)
Kahng, Byungik
Issue Date
2000
Doctoral Committee Chair(s)
Palmore, Julian
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
We investigate the iterative dynamics of symplectic piecewise-affine elliptic rotation maps associated with matrices with non-integer entries, 0-11a , where -2 < a < 2. We explain how their singularity and periodicity structures develop in general. In a special case, a = +/- 2 , we completely determine the orbit structure and the singularity structure, and answer conjectures by Tresser, Adler and Kitchens. We also report an example of a period tripling cascade that arises from this system.
Graduation Semester
2000
Type of Resource
text
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http://hdl.handle.net/2142/87003

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