The relation between the size of perturbations and the dimension of tori in an infinite-dimensional KAM theorem of Pöschel

Abstract

In this paper, we discuss the relation between the size of perturbations and the dimension of tori based on the KAM theorem of Pöschel (1996) which can be applied to infinite dimensional PDEs, in other words, we give a quantitative version of the KAM theorem of Pöschel (1996). Moreover, motivated by Chung and Yuan (2007, 2008) and Li and Yuan (2012), after infinite KAM iterations, we make action and normal variables of KAM tori of the reduced Hamiltonian system in a domain instead of shrinking them to the origin.