Lie symmetries of birational maps preserving genus 0 fibrations

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/26449

Title:	Lie symmetries of birational maps preserving genus 0 fibrations
Author:	Llorens, Mireia; Mañosa Fernández, Víctor
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions
Abstract:	Preprint.
Abstract:	We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics of these maps. Using this approach, the dynamics of several maps is described. In particular we are able to give, for particular examples, the explicit expression of the rotation number function, and the set of periods of the considered maps.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals -Differentiable dynamical systems -Foliations (Mathematics) -Integrable maps -Lie symmetries -Periodic orbits -Rational parameterizations. -Sistemes dinàmics diferenciables -Foliacions (Matemàtica) -Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory -Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems -Classificació AMS::39 Difference and functional equations::39A Difference equations
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Draft Report
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