Numerical study of invariant sets of a volume - preserving map

Stathis Tompaidis 1 2 IRMAR Universit e de Rennes I 35042 Rennes Cedex France Abstract. We study the behavior of invariant sets of a volume-preserving map, that is a quasi-periodic perturbation of a symplectic map, using approximation by periodic orbits. We present numerical results for analyticity domains of invariant surfaces, behavior after breakdown and a critical function describing breakdown of invariant surfaces as a function of their rotation vectors. We discuss implications of our results to the existence of a renormalization group operator describing breakdown of invariant surfaces.