Continua of periodic points for planar integrable rational maps

We present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used by other authors and apply when the maps are birational and the generic level sets of the corresponding firs...

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Authors: Gasull Embid, Armengol, Llorens, Mireia, Mañosa Fernández, Víctor|||0000-0002-5082-3334
Format: article
Publication Date:2016
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/90779
Online Access:https://hdl.handle.net/2117/90779
Access Level:Open access
Keyword:Differentiable dynamical systems
Differential equations
Integrable rational maps
Birational maps
Periodic orbits
Sistemes dinàmics diferenciables
Equacions diferencials ordinàries
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Classificació AMS::39 Difference and functional equations::39A Difference equations
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
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oai_identifier_str oai:upcommons.upc.edu:2117/90779
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repository_id_str
spelling Continua of periodic points for planar integrable rational mapsGasull Embid, ArmengolLlorens, MireiaMañosa Fernández, Víctor|||0000-0002-5082-3334Differentiable dynamical systemsDifferential equationsIntegrable rational mapsBirational mapsPeriodic orbitsSistemes dinàmics diferenciablesEquacions diferencials ordinàriesClassificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theoryClassificació AMS::39 Difference and functional equations::39A Difference equationsÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integralsWe present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used by other authors and apply when the maps are birational and the generic level sets of the corresponding first integrals have either genus 0 or 1. As far as we know, the third one is new and it works for rational maps without imposing topological properties to the invariant level sets. It is based on a computational point of view, and relies on the use of resultants in a suitable setting. We apply them to several examples, including the 2-periodic Lyness composition maps and some of the celebrated McMillan–Gumovski–Mira mapsPeer ReviewedResearch India Publications20162016-09-0120162016-10-14journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/90779reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/907792026-05-27T15:37:01Z
dc.title.none.fl_str_mv Continua of periodic points for planar integrable rational maps
title Continua of periodic points for planar integrable rational maps
spellingShingle Continua of periodic points for planar integrable rational maps
Gasull Embid, Armengol
Differentiable dynamical systems
Differential equations
Integrable rational maps
Birational maps
Periodic orbits
Sistemes dinàmics diferenciables
Equacions diferencials ordinàries
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Classificació AMS::39 Difference and functional equations::39A Difference equations
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
title_short Continua of periodic points for planar integrable rational maps
title_full Continua of periodic points for planar integrable rational maps
title_fullStr Continua of periodic points for planar integrable rational maps
title_full_unstemmed Continua of periodic points for planar integrable rational maps
title_sort Continua of periodic points for planar integrable rational maps
dc.creator.none.fl_str_mv Gasull Embid, Armengol
Llorens, Mireia
Mañosa Fernández, Víctor|||0000-0002-5082-3334
author Gasull Embid, Armengol
author_facet Gasull Embid, Armengol
Llorens, Mireia
Mañosa Fernández, Víctor|||0000-0002-5082-3334
author_role author
author2 Llorens, Mireia
Mañosa Fernández, Víctor|||0000-0002-5082-3334
author2_role author
author
dc.subject.none.fl_str_mv Differentiable dynamical systems
Differential equations
Integrable rational maps
Birational maps
Periodic orbits
Sistemes dinàmics diferenciables
Equacions diferencials ordinàries
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Classificació AMS::39 Difference and functional equations::39A Difference equations
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
topic Differentiable dynamical systems
Differential equations
Integrable rational maps
Birational maps
Periodic orbits
Sistemes dinàmics diferenciables
Equacions diferencials ordinàries
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Classificació AMS::39 Difference and functional equations::39A Difference equations
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
description We present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used by other authors and apply when the maps are birational and the generic level sets of the corresponding first integrals have either genus 0 or 1. As far as we know, the third one is new and it works for rational maps without imposing topological properties to the invariant level sets. It is based on a computational point of view, and relies on the use of resultants in a suitable setting. We apply them to several examples, including the 2-periodic Lyness composition maps and some of the celebrated McMillan–Gumovski–Mira maps
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-09-01
2016
2016-10-14
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/90779
url https://hdl.handle.net/2117/90779
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Research India Publications
publisher.none.fl_str_mv Research India Publications
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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