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University of Illinois at Urbana-Champaign
Dynamics of Symplectic Piecewise Affine Elliptic Rotation Maps on Tori
Abstract
dc:descriptionWe 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Kahng, Byungik
- Contributors dc:contributor
-
- Palmore, Julian
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI9990033
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/87003