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.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/7221 |
| Date | 19 July 2005 |
| Creators | Moeller, Todd Keith |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | 498877 bytes, application/pdf |
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