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Title:
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Continua of periodic points for planar integrable rational maps.
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Author:
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Gasull Embid, Armengol; Llorens, Mireia; Mañosa Fernández, Víctor
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
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Abstract:
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Prepublicació |
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Abstract:
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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. |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
-Differentiable dynamical systems
-Differential equations
-Periodic orbits
-Integrable rational maps
-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 |
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Rights:
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Document type:
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Article - Draft
Report |
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