Periodic points of a Landen transformation

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/112835

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions
dc.contributor.author	Gasull Embid, Armengol
dc.contributor.author	Llorens, Mireia
dc.contributor.author	Mañosa Fernández, Víctor
dc.date	2018-01-12
dc.identifier.citation	Gasull, A., Llorens, M., Mañosa, V. "Periodic points of a Landen transformation". 2018.
dc.identifier.uri	http://hdl.handle.net/2117/112835
dc.language.iso	eng
dc.relation	arXiv:1801.04195 [math.DS]
dc.relation	https://arxiv.org/abs/1801.04195
dc.relation	info:eu-repo/grantAgreement/ES/1PE/DPI2016-77407-P
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
dc.subject	Differentiable dynamical systems
dc.subject	Periodic points
dc.subject	Periodic orbits
dc.subject	Discrete dynamical systems
dc.subject	Landen transformations
dc.subject	homoclinic points
dc.subject	Sistemes dinàmics diferenciables
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
dc.subject	Classificació AMS::33 Special functions::33E Other special functions
dc.title	Periodic points of a Landen transformation
dc.type	info:eu-repo/semantics/draft
dc.type	info:eu-repo/semantics/report
dc.description.abstract	Preprint
dc.description.abstract	We prove the existence of 3-periodic orbits in a dynamical system associated to a Landen transformation previously studied by Boros, Chamberland and Moll, disproving a conjecture on the dynamics of this planar map introduced by the latter author. To this end we present a systematic methodology to determine and locate analytically isolated periodic points of algebraic maps. This approach can be useful to study other discrete dynamical systems with algebraic nature. Complementary results on the dynamics of the map associated with the Landen transformation are also presented.

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