Ricardo Pérez-Marco Department of Mathematics University of California Los Angeles, CA 90024 USA E-mail address: ricardo@math.ucla.edu

KAM theory in Infinite Dimensional Spaces

Abstract: KAM theory is one of the two major theories in Dynamical Systems developped during the XXth Century. Its scope reaches other fields as Riemannian Geometry, PDE and Functional Analisis. For example, it did motivate Hamilton Local Inversion Theorem in Good Frechet spaces. Our purpose is to describe recent developments of KAM theory to Hamiltonian systems in Infinite Dimensional spaces.