{"id":{"repo_id":"queens","oai_identifier":"oai:queensu.scholaris.ca:1974/8288"},"canonical_url":"https://search.dev.ndltd.org/etd/queens/oai:queensu.scholaris.ca:1974/8288","repository":{"repo_id":"queens","name":"Queens University","base_url":"https://qspace.library.queensu.ca/server/oai/request"},"display":{"title":"Homoclinic Points in the Composition of Two Reflections","abstract":"We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \\to R$ be $C^1$ functions with domain all of $R$. Let $F:R^2 \\to R^2$ denote a horizontal reflection in the curve $x=-f(y)$, and let $G:R^2 \\to R^2$ denote a vertical reflection in the curve $y=g(x)$. We consider maps of the form $T=G \\circ F$ and show that a simple geometric condition on the fixed point sets of $F$ and $G$ leads to the existence of a homoclinic point for $T$.","abstract_html":"We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \\to R$ be <span class=\"etd-inline-math\">C<sup>1</sup></span> functions with domain all of $R$. Let <span class=\"etd-inline-math\">F:R<sup>2</sup> \\to R<sup>2</sup></span> denote a horizontal reflection in the curve $x=-f(y)$, and let <span class=\"etd-inline-math\">G:R<sup>2</sup> \\to R<sup>2</sup></span> denote a vertical reflection in the curve $y=g(x)$. We consider maps of the form $T=G \\circ F$ and show that a simple geometric condition on the fixed point sets of $F$ and $G$ leads to the existence of a homoclinic point for $T$.","abstract_has_math":true,"creators":["Jensen, Erik"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Mathematics and Statistics","school":null,"contributors":[],"advisors":["Offin, Daniel"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-09-17","date_published":"2013-09-17","updated_at":"2026-07-27T20:35:21Z","subjects":["Area Preserving Maps","Homoclinic Points","Mathematics","Dynamical Systems"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1974/8288","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mathematics and Statistics"]},{"key":"dc:contributor.supervisor","label":"Supervisor","values":["Offin, Daniel"]},{"key":"dc:creator","label":"Author","values":["Jensen, Erik"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-09-17 14:22:35.72"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-09-17T20:35:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-09-17T20:35:28Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-09-17"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Area Preserving Maps","Homoclinic Points","Mathematics","Dynamical Systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1974/8288"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-17 14:22:35.72"]},{"key":"dc:description.abstract","label":"Abstract","values":["We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \\to R$ be $C^1$ functions with domain all of $R$. Let $F:R^2 \\to R^2$ denote a horizontal reflection in the curve $x=-f(y)$, and let $G:R^2 \\to R^2$ denote a vertical reflection in the curve $y=g(x)$. We consider maps of the form $T=G \\circ F$ and show that a simple geometric condition on the fixed point sets of $F$ and $G$ leads to the existence of a homoclinic point for $T$."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["PhD"]},{"key":"dc:title","label":"Title","values":["Homoclinic Points in the Composition of Two Reflections"]}]}],"canonical_facts":{"dc:contributor.department":["Mathematics and Statistics"],"dc:contributor.supervisor":["Offin, Daniel"],"dc:creator":["Jensen, Erik"],"dc:date":["2013-09-17 14:22:35.72"],"dc:date.accessioned":["2013-09-17T20:35:28Z"],"dc:date.available":["2013-09-17T20:35:28Z"],"dc:date.issued":["2013-09-17"],"dc:description":["Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-17 14:22:35.72"],"dc:description.abstract":["We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \\to R$ be $C^1$ functions with domain all of $R$. Let $F:R^2 \\to R^2$ denote a horizontal reflection in the curve $x=-f(y)$, and let $G:R^2 \\to R^2$ denote a vertical reflection in the curve $y=g(x)$. We consider maps of the form $T=G \\circ F$ and show that a simple geometric condition on the fixed point sets of $F$ and $G$ leads to the existence of a homoclinic point for $T$."],"dc:description.degree":["PhD"],"dc:identifier.uri":["http://hdl.handle.net/1974/8288"],"dc:language.iso":["eng"],"dc:subject":["Area Preserving Maps","Homoclinic Points","Mathematics","Dynamical Systems"],"dc:title":["Homoclinic Points in the Composition of Two Reflections"],"dc:type":["thesis"]},"updated_at":"2026-07-27T20:35:21Z"}