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    Conley-Morse Chain Maps

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    moeller_todd_k_200508_phd.pdf (487.1Kb)
    Date
    2005-07-19
    Author
    Moeller, Todd Keith
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    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.
    URI
    http://hdl.handle.net/1853/7221
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    • Georgia Tech Theses and Dissertations [23403]
    • School of Mathematics Theses and Dissertations [424]

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