Existence Of Invariant Curves For Area-preserving Mappings Under Weaker Non-degeneracy Conditions

Abstract:This paper considers two-dimensional area preserving mappingswhere f(?,x,y)and g(?,x,y)are real analytic in x,y and periodic with respect to x,?T,|y|?r.Moreover,they are Cm smooth with respect to the parameter?.If the perturbation is sufficiently small,by KAM iteration we prove a formal KAM theorem without any non-degeneracy assumption.In particular,our theorem can be used to prove some previous KAM-type results and obtain some new inter-esting results under various kinds of non-degeneracy conditions and non-resonance conditions.