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Periodic orbits of planar integrable birational maps

Author
Galvez, M.; Mañosa, V.
Type of activity
Report
Date
2014-02-14
Project funding
Análisis e identificación de sistemas con histéresis usando órbitas periódicas
CONTROL, DINÀMICA I APLICACIONS (CODALAB)
Geomatría algebraica, simpléctica, aritmética y aplicaciones.
Repository
http://hdl.handle.net/2117/21748 Open in new window
Abstract
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. A birational planar map F possessing a rational firs...
Citation
Galvez, M.; Mañosa, V. "Periodic orbits of planar integrable birational maps". 2014.
Keywords
Algebraic geometry, Birational maps, Discrete dynamical systems, Elliptic curves, Integrable maps, Periodic orbits.
Group of research
CoDAlab - Control, Dynamics and Applications
GEOMVAP - Geometry of Manifolds and Applications

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