{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71228"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71228","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Strange Attractors of Uniform Flows (Cantor Set, Solenoid)","abstract":"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).","abstract_html":"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).","abstract_has_math":false,"creators":["Kan, Ittai"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:12Z","date_published":"2014-12-16T06:18:12Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8502197"],"render_values":[{"text":"(UMI)AAI8502197","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71228","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kan, Ittai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:12Z","10000-01-01","1984"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71228","(UMI)AAI8502197"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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).","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). No. of bitstreams: 1 8502197.pdf: 1401414 bytes, checksum: 156bb71db3535e6fd82be07dbefb31b8 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 71394 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","53 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."]},{"key":"dc:title","label":"Title","values":["Strange Attractors of Uniform Flows (Cantor Set, Solenoid)"]}]}],"canonical_facts":{"dc:creator":["Kan, Ittai"],"dc:date":["2014-12-16T06:18:12Z","10000-01-01","1984"],"dc:description":["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).","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). No. of bitstreams: 1 8502197.pdf: 1401414 bytes, checksum: 156bb71db3535e6fd82be07dbefb31b8 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 71394 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","53 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."],"dc:identifier":["http://hdl.handle.net/2142/71228","(UMI)AAI8502197"],"dc:subject":["Mathematics"],"dc:title":["Strange Attractors of Uniform Flows (Cantor Set, Solenoid)"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:04Z"}