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Lie symmetries of birational maps preserving genus 0 fibrations
Llorens, Mireia; Mañosa Fernández, Víctor
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. CODALAB - Control, Dinàmica i Aplicacions
Preprint.
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.
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Article - Draft
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