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...
| Autores: | , |
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| 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 |
| 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. |
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