Periodic orbits of planar integrable birational maps

A birational planar map F possessing a rational first integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically genus 0 or 1. In the genus 1 case, the group structure of the foliation characteriz...

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Detalles Bibliográficos
Autores: Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437, Mañosa Fernández, Víctor|||0000-0002-5082-3334
Tipo de recurso: informe técnico
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/21748
Acceso en línea:https://hdl.handle.net/2117/21748
Access Level:acceso abierto
Palabra clave:Geometry, Algebraic
Discrete dynamical systems
Algebraic geometry
Birational maps
Integrable maps
Elliptic curves
Periodic orbits.
Geometria algebraica
Sistemes no lineals
Classificació AMS::14 Algebraic geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Descripción
Sumario:A birational planar map F possessing a rational first integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically genus 0 or 1. In the genus 1 case, the group structure of the foliation characterizes the dynamics of any birational map preserving it. We will see how to take advantage of this structure to find periodic orbits of such maps.