Continua of periodic points for planar integrable rational maps
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llorens, Mireia (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)

Date:	2016
Abstract:	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 for 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-Gumowski-Mira maps.
Grants:	Ministerio de Ciencia e Innovación PN2008-2011/DPI2011-25822 Agència de Gestió d'Ajuts Universitaris i de Recerca PRI2010-2013 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014-SGR-859
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Birational maps ; Integrable rational maps ; Periodic orbits
Published in:	International Journal of Difference Equations, Vol. 11 Núm. 1 (2016) , p. 37-63, ISSN 0973-6069

Postprint 26 p, 508.8 KB

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