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dc.contributor.authorMoeller, Todd Keithen_US
dc.date.accessioned2005-09-16T15:14:58Z
dc.date.available2005-09-16T15:14:58Z
dc.date.issued2005-07-19en_US
dc.identifier.urihttp://hdl.handle.net/1853/7221
dc.description.abstractWe 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.format.extent498877 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectConley indexen_US
dc.subjectMorse theory
dc.subjectData analysis
dc.subject.lcshMathematical statisticsen_US
dc.subject.lcshMorse theoryen_US
dc.subject.lcshAlgebraic topologyen_US
dc.subject.lcshHomology theoryen_US
dc.titleConley-Morse Chain Mapsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Konstantin Mischaikow; Committee Member: Greg Turk; Committee Member: Guillermo Goldsztein; Committee Member: Margaret Symington; Committee Member: William Greenen_US


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