Type of Document	Dissertation
Author	Moeller, Todd Keith
Author's Email Address	moeller@math.gatech.edu
URN	etd-07152005-144331
Title	Conley-Morse Chain Maps
Degree	Doctor of Philosophy
Department	Mathematics
Advisory Committee	Advisor Name Title Konstantin Mischaikow Committee Chair Greg Turk Committee Member Guillermo Goldsztein Committee Member Margaret Symington Committee Member William Green Committee Member
Keywords	Conley index Morse theorey data analysis
Date of Defense	2005-07-14
Availability	unrestricted
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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