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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Detalles Bibliográficos
Autores: Llorens, Mireia, Mañosa Fernández, Víctor|||0000-0002-5082-3334
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:145297
Acceso en línea:https://ddd.uab.cat/record/145297
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2015.06.069
Access Level:acceso abierto
Palabra clave:Integrable maps
Lie symmetries
Periodic orbit
Rational parameterizations
Descripción
Sumario: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.