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 STYLE
Gálvez-Carrillo, I., & Mañosa, V. (2015). Periodic orbits of planar integrable birational maps. In Springer Proceedings in Mathematics and Statistics (Vol. 112, pp. 13–36). Springer New York LLC. https://doi.org/10.1007/978-3-319-12328-8_2
Mendeley helps you to discover research relevant for your work.