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Computing topological dynamics from time series
 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, 18841972 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 