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Dissertation
Topological aspects of the structure of chaotic attractors in R³
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2004
DOI:
https://doi.org/10.17918/etd-304
Abstract
We extend the methods for topological analysis of chaotic dynamical systems in R³ by introducing two new concepts - embedding manifolds and their canonical forms. These are used to specify in topological terms the large scale global structure of chaotic attracting sets. We show how these ideas help us put the finishing touch on the third coarsest level in a classification scheme for strange attractors in R³, for which the two lower levels have been constructed about a decade ago. In addition we present a guide on how to construct a Poincare surface of section for strange attractors with Lyapunov dimension d_L<3. We show how to extract information about the canonical form from scalar time series. In addition we discuss what possible changes occur to the topological properties of the unstable periodic orbits in the strange attractor, as we use different embedding mappings into R³.
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Details
- Title
- Topological aspects of the structure of chaotic attractors in R³
- Creators
- Tsvetelin Draganov Tsankov - DU
- Contributors
- Robert Gilmore (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Physics; Drexel University
- Other Identifier
- 304; 991014632194604721