Periodic orbits of planar integrable birational maps, part I: the elliptic case [ Back ]

Date:
27.03.17   
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Víctor Mañosa
University:
Universitat Politècnica de Catalunya

Abstract:

We will consider birational planar maps possessing a rational first integral so that they preserve a foliation of the plane given by algebraic curves which have generically genus 1 (they are elliptic curves). In this 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 and we will see some related problems.

The talk will we as general as possible and addressed to a wide audience. The worked examples come from joint works with G. Bastien, A. Cima, I. Gálvez, A. Gasull, M. Llorens, M. Rogalski, and X. Xarles.