Title:
Conley-Morse Chain Maps
Conley-Morse Chain Maps
| dc.contributor.advisor | Mischaikow, Konstantin | |
| dc.contributor.author | Moeller, Todd Keith | en_US |
| dc.contributor.committeeMember | Greg Turk | |
| dc.contributor.committeeMember | Guillermo Goldsztein | |
| dc.contributor.committeeMember | Margaret Symington | |
| dc.contributor.committeeMember | William Green | |
| dc.contributor.department | Mathematics | en_US |
| dc.date.accessioned | 2005-09-16T15:14:58Z | |
| dc.date.available | 2005-09-16T15:14:58Z | |
| dc.date.issued | 2005-07-19 | en_US |
| dc.description.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. | en_US |
| dc.description.degree | Ph.D. | en_US |
| dc.format.extent | 498877 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/7221 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | en_US |
| dc.subject | Conley index | en_US |
| dc.subject | Morse theory | |
| dc.subject | Data analysis | |
| dc.subject.lcsh | Mathematical statistics | en_US |
| dc.subject.lcsh | Morse theory | en_US |
| dc.subject.lcsh | Algebraic topology | en_US |
| dc.subject.lcsh | Homology theory | en_US |
| dc.title | Conley-Morse Chain Maps | en_US |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 |
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