Lie symmetries of birational maps preserving genus 0 fibrations

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 m...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 432; no. 1; pp. 531 - 549
Main Authors: Llorens, Mireia, Mañosa, Víctor
Format: Journal Article Publication
Language:English
Published: Elsevier Inc 01.12.2015
Subjects:
37 Dynamical systems and ergodic theory
37C Smooth dynamical systems: general theory
37E Low-dimensional dynamical systems
39 Difference and functional equations
39A Difference equations
Classificació AMS
Differentiable dynamical systems
Equacions diferencials i integrals
Foliacions (Matemàtica)
Foliations (Mathematics)
Integrable maps
Lie symmetries
Matemàtiques i estadística
Periodic orbits
Rational parameterizations
Sistemes dinàmics diferenciables
Àrees temàtiques de la UPC
Integrable maps
Periodic orbits
Lie symmetries
Rational parameterizations
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.06.069