{"id":{"repo_id":"east-anglia","oai_identifier":"oai:ueaeprints.uea.ac.uk:54400"},"canonical_url":"https://search.dev.ndltd.org/etd/east-anglia/oai:ueaeprints.uea.ac.uk:54400","repository":{"repo_id":"east-anglia","name":"University of East Anglia","base_url":"https://ueaeprints.uea.ac.uk/cgi/oai2"},"display":{"title":"Closed orbits in quotient systems","abstract":"If we have topological conjugacy between two continuous maps, T : X → X and T 0 : X0 → X0 , then counts of closed orbits and periodic points are preserved. However, if we only have topological semi-conjugacy between T and T 0 , then anything is possible, and there is, in general, no relationship between closed orbits (or periodic points) of T and T 0 . However, if we let a finite group G act on X, where the action of G commutes with T and where we let X0 = G\\X be the quotient of the action, then it is indeed possible to say a bit more about the relationship between the count of closed orbits of (X, T) and its quotient system (X0 , T0 ). In this thesis, we will describe the behaviour of closed orbits in quotient systems, and we will show that there exists a wide but restricted range of what growth rates can be achieved for these orbits. Moreover, we will examine the analytic properties of the dynamical zeta function in quotient systems.","abstract_html":"If we have topological conjugacy between two continuous maps, T : X → X and T 0 : X0 → X0 , then counts of closed orbits and periodic points are preserved. However, if we only have topological semi-conjugacy between T and T 0 , then anything is possible, and there is, in general, no relationship between closed orbits (or periodic points) of T and T 0 . However, if we let a finite group G act on X, where the action of G commutes with T and where we let X0 = G\\X be the quotient of the action, then it is indeed possible to say a bit more about the relationship between the count of closed orbits of (X, T) and its quotient system (X0 , T0 ). In this thesis, we will describe the behaviour of closed orbits in quotient systems, and we will show that there exists a wide but restricted range of what growth rates can be achieved for these orbits. Moreover, we will examine the analytic properties of the dynamical zeta function in quotient systems.","abstract_has_math":false,"creators":["Zegowitz, Stefanie"],"institution":"University of East Anglia","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01","date_published":"2015-01","updated_at":"2026-07-24T02:12:10Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Zegowitz, Stefanie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-01"]},{"key":"dc:date.issued","label":"Date","values":["2015-01"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of East Anglia"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://ueaeprints.uea.ac.uk/id/eprint/54400/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://ueaeprints.uea.ac.uk/id/eprint/54400/1/2015ZegowitzSPhD.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["If we have topological conjugacy between two continuous maps, T : X → X and T 0 : X0 → X0 , then counts of closed orbits and periodic points are preserved. However, if we only have topological semi-conjugacy between T and T 0 , then anything is possible, and there is, in general, no relationship between closed orbits (or periodic points) of T and T 0 . However, if we let a finite group G act on X, where the action of G commutes with T and where we let X0 = G\\X be the quotient of the action, then it is indeed possible to say a bit more about the relationship between the count of closed orbits of (X, T) and its quotient system (X0 , T0 ). In this thesis, we will describe the behaviour of closed orbits in quotient systems, and we will show that there exists a wide but restricted range of what growth rates can be achieved for these orbits. Moreover, we will examine the analytic properties of the dynamical zeta function in quotient systems."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Closed orbits in quotient systems"]}]}],"canonical_facts":{"dc:creator":["Zegowitz, Stefanie"],"dc:date":["2015-01"],"dc:date.issued":["2015-01"],"dc:description.abstract":["If we have topological conjugacy between two continuous maps, T : X → X and T 0 : X0 → X0 , then counts of closed orbits and periodic points are preserved. However, if we only have topological semi-conjugacy between T and T 0 , then anything is possible, and there is, in general, no relationship between closed orbits (or periodic points) of T and T 0 . However, if we let a finite group G act on X, where the action of G commutes with T and where we let X0 = G\\X be the quotient of the action, then it is indeed possible to say a bit more about the relationship between the count of closed orbits of (X, T) and its quotient system (X0 , T0 ). In this thesis, we will describe the behaviour of closed orbits in quotient systems, and we will show that there exists a wide but restricted range of what growth rates can be achieved for these orbits. Moreover, we will examine the analytic properties of the dynamical zeta function in quotient systems."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://ueaeprints.uea.ac.uk/id/eprint/54400/1/2015ZegowitzSPhD.pdf"],"dc:language":["en"],"dc:publisher.department":["School of Mathematics"],"dc:publisher.institution":["University of East Anglia"],"dc:relation.isreferencedby":["https://ueaeprints.uea.ac.uk/id/eprint/54400/"],"dc:title":["Closed orbits in quotient systems"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T02:12:10Z"}