{"id":{"repo_id":"uvic","oai_identifier":"oai:dspace.library.uvic.ca:1828/1257"},"canonical_url":"https://search.dev.ndltd.org/etd/uvic/oai:dspace.library.uvic.ca:1828/1257","repository":{"repo_id":"uvic","name":"University of Victoria (Canada)","base_url":"https://dspace.library.uvic.ca/server/oai/request"},"display":{"title":"On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators","abstract":"The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms on a Banach lattice. In this paper, it is verified directly that the peripheral point spectrum of the Frobenius-Perron operator and the point spectrum of the Koopman operator are fully cyclic. Under some restrictions on the underlying transformation, the Frobenius-Perron operator is known to be a well defined linear operator on the Banach space of functions of bounded variation. It is also shown that the peripheral point spectrum of the Frobenius-Perron operator on the functions of bounded variation is fully cyclic.","abstract_html":"The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms on a Banach lattice. In this paper, it is verified directly that the peripheral point spectrum of the Frobenius-Perron operator and the point spectrum of the Koopman operator are fully cyclic. Under some restrictions on the underlying transformation, the Frobenius-Perron operator is known to be a well defined linear operator on the Banach space of functions of bounded variation. It is also shown that the peripheral point spectrum of the Frobenius-Perron operator on the functions of bounded variation is fully cyclic.","abstract_has_math":false,"creators":["Sorge, Joshua"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Bose, Christopher"],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-11-17T23:03:01Z","date_published":"2008-11-17T23:03:01Z","updated_at":"2026-08-21T16:50:31Z","subjects":["Frobenius-Perron operator","Koopman operator","cyclic"],"languages":["en","English"],"rights":["Available to the World Wide Web"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1828/1257","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://dspace.library.uvic.ca/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Adspace.library.uvic.ca%3A1828%2F1257","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.supervisor","label":"Supervisor","values":["Bose, Christopher"]},{"key":"dc:creator","label":"Author","values":["Sorge, Joshua"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2008-11-17T23:03:01Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2008-11-17T23:03:01Z"]},{"key":"dc:date.issued","label":"Date","values":["2008-11-17T23:03:01Z"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Frobenius-Perron operator","Koopman operator","cyclic"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Available to the World Wide Web"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1828/1257"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms on a Banach lattice. In this paper, it is verified directly that the peripheral point spectrum of the Frobenius-Perron operator and the point spectrum of the Koopman operator are fully cyclic. Under some restrictions on the underlying transformation, the Frobenius-Perron operator is known to be a well defined linear operator on the Banach space of functions of bounded variation. It is also shown that the peripheral point spectrum of the Frobenius-Perron operator on the functions of bounded variation is fully cyclic."]},{"key":"dc:title","label":"Title","values":["On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators"]}]}],"canonical_facts":{"dc:contributor.supervisor":["Bose, Christopher"],"dc:creator":["Sorge, Joshua"],"dc:date.accessioned":["2008-11-17T23:03:01Z"],"dc:date.available":["2008-11-17T23:03:01Z"],"dc:date.issued":["2008-11-17T23:03:01Z"],"dc:description.abstract":["The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms on a Banach lattice. In this paper, it is verified directly that the peripheral point spectrum of the Frobenius-Perron operator and the point spectrum of the Koopman operator are fully cyclic. Under some restrictions on the underlying transformation, the Frobenius-Perron operator is known to be a well defined linear operator on the Banach space of functions of bounded variation. It is also shown that the peripheral point spectrum of the Frobenius-Perron operator on the functions of bounded variation is fully cyclic."],"dc:identifier.uri":["http://hdl.handle.net/1828/1257"],"dc:language":["English"],"dc:language.iso":["en"],"dc:rights":["Available to the World Wide Web"],"dc:subject":["Frobenius-Perron operator","Koopman operator","cyclic"],"dc:title":["On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators"],"dc:type":["Thesis"]},"updated_at":"2026-08-21T16:50:31Z"}