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Classification of Linear Flows Open Access

Descriptions

Other title
Subject/Keyword
flow equivalence
dynamical systems
linear flow
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Wynne, Anthony A
Supervisor and department
Berger, Arno (Mathematical and Statistical Sciences)
Examining committee member and department
Berger, Arno (Mathematical and Statistical Sciences)
Pass, Brendan (Mathematical and Statistical Sciences)
Hillen, Thomas (Mathematical and Statistical Sciences)
Runde, Volker (Mathematical and Statistical Sciences)
Gille, Stefan (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2016-01-15T09:06:02Z
Graduation date
2016-06
Degree
Master of Science
Degree level
Master's
Abstract
Flows on normed spaces can be classified using flow equivalences --- maps on the space with the property that the structure of one flow is converted into the structure of another flow. Of particular interest are classifications that arise from flow equivalences that are either homeomorphisms or diffeomorphisms. It is possible to completely characterize such classifications based solely on a few simple properties of flows, at least in the case of linear flows on finite-dimensional normed spaces. Results concerning diffeomorphic classification are well known and can be found in many textbooks that discuss continuous dynamical systems. The situation is similar when it comes to homeomorphic classification of hyperbolic flows, but for arbitrary (possibly nonhyperbolic) flows results concerning homeomorphic classification are fairly obscure. This thesis aims to provide a complete discussion of the homeomorphic and diffeomorphic classification of linear flows on finite-dimensional normed spaces.
Language
English
DOI
doi:10.7939/R3NG4H333
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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