Title:
Conley-Morse Chain Maps
Conley-Morse Chain Maps
Authors
Moeller, Todd Keith
Advisors
Mischaikow, Konstantin
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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.
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Date Issued
2005-07-19
Extent
498877 bytes
Resource Type
Text
Resource Subtype
Dissertation