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Computing topological dynamics from time series

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Date Issued:
2008
Summary:
The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series.
Title: Computing topological dynamics from time series.
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Name(s): Wess, Mark.
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Issued: 2008
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: ix, 98 p. : ill. (some col.).
Language(s): English
Summary: The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series.
Identifier: 317620750 (oclc), 186294 (digitool), FADT186294 (IID), fau:2861 (fedora)
Note(s): by Mark Wess.
Thesis (Ph.D.)--Florida Atlantic University, 2008.
Includes bibliography.
Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.
Subject(s): Lefschetz, Solomon, 1884-1972
Algebraic topology
Graph theory
Fixed point theory
Singularities (Mathematics)
Persistent Link to This Record: http://purl.flvc.org/FAU/186294
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Owner Institution: FAU