Date of Award
2008
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
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.
Extent
ix, 98 p. : ill. (some col.).
Recommended Citation
Wess, Mark., "Computing topological dynamics from time series" (2008). Electronic Theses and Dissertations 2000 - 2009. 1433.
https://digitalcommons.fau.edu/etd_general_5/1433
Identifier
FADT186294
Comments
by Mark Wess.|Thesis (Ph.D.)--Florida Atlantic University, 2008.|Includes bibliography.|Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.|by Mark Wess.