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...
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 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.
Citation
Galvez, M.; Mañosa, V. "Periodic orbits of planar integrable birational maps". 2014.