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moeller_todd_k_200508_phd.pdf (487.18 KB)

Author(s)

Moeller, Todd Keith

Authors

Advisor(s)

Mischaikow, Konstantin

Advisor(s)

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Associated Organization(s)

Organizational Unit

College of Sciences

Organizational Unit

School of Mathematics

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Theses and Dissertations

Supplementary to

Permanent Link

http://hdl.handle.net/1853/7221

Abstract

We introduce a new class of Conley-Morse chain maps for the purpose of comparing the qualitative structure of flows across multiple scales. Conley index theory generalizes classical Morse theory as a tool for studying the dynamics of flows. The qualitative structure of a flow, given a Morse decomposition, can be stored algebraically as a set of homology groups (Conley indices) and a boundary map between the indices (a connection matrix). We show that as long as the qualitative structures of two flows agree on some, perhaps coarse, level we can construct a chain map between the corresponding chain complexes that preserves the relations between the (coarsened) Morse sets. We present elementary examples to motivate applications to data analysis.

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Date Issued

2005-07-19

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498877 bytes

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Text

Resource Subtype

Dissertation

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