Strange Attractors of Uniform Flows (Cantor Set, Solenoid)

Consider orbitally stable attractors of those flows on the open solid torus D('2) x S('1) which have uniform velocity in the S('1) direction (uniform flows). It was found that any such attractor is the frontier of a strictly nested sequence of positively invariant open solid tori. Necessary and sufficient conditions related to these tori are derived for an arbitrary set to be an orbitally stable attractor. When the cross-section of an orbitally stable attractor is a Cantor set, then first return map is found to be conjugate to an irrational rotation on a certain compact abelian group. New examples are constructed of orbitally stable attractors of uniform C('(INFIN)) flows whose cross-sections have uncountably many components (one of these attractors has positive 3-dimensional Lebesgue measure).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Kan, Ittai

• Mathematics

Identifier

(UMI)AAI8502197

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71228