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Computing topological dynamics from time series

Author: Mark Wess
Publisher: 2008.
Dissertation: Thesis (Ph.D.)--Florida Atlantic University, 2008.
Edition/Format:   Thesis/dissertation : Thesis/dissertation : EnglishView all editions and formats
Database:WorldCat
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  Read more...
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Named Person: Solomon Lefschetz; Solomon Lefschetz
Material Type: Thesis/dissertation
Document Type: Book
All Authors / Contributors: Mark Wess
OCLC Number: 317620750
Reproduction Notes: Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.
Description: ix, 98 p. : ill. (some col.)
Responsibility: by Mark Wess.

Abstract:

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.

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