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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical analysis and applications Jg. 432; H. 1; S. 531 - 549
Hauptverfasser: Llorens, Mireia, Mañosa, Víctor
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.12.2015
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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