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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