Abstract

We consider birational maps F(x) , xin R^k having k - 1 rational first integrals functionally independent and we determine the dynamics of every x in R^k such that F^n is well defined for all n in Z. Fixed a level set, we do a process of compactification and desingularitation getting a finite number of circles and closed intervals. We extend the map in such a way that for some iterates of F each circle and each interval is invariant, getting the standard dynamics of orientation preserving homeomorphisms on the circle and on the closed intervals. In the second part of the talk we add a new ingredient: the existence of a Lie symmetry of the map. When all the objects are rational we give a more accurate description of the dynamics on the level sets.

This is a joint work with Francesc Mañosas