A Classification of Kupka-Smale Flows on the Torus
Gardiner, Christopher John
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https://hdl.handle.net/2142/68187
Description
Title
A Classification of Kupka-Smale Flows on the Torus
Author(s)
Gardiner, Christopher John
Issue Date
1981
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
This thesis presents a classification up to topological equivalence of those flows on the torus satisfying: (1) all singular points and closed orbits are hyperbolic; and (2) there are no saddle connections. Such flows are known as Kupka-Smale flows. In the process of generating invariants for the classification a qualitative picture is produced describing the structure of such flows in the case that they possess a limit set which is neither a singular point nor a closed orbit.
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