Resumen de Persistence of Lower Dimensional Hyperbolic Invariant Tori for Nearly Integrable Symplectic Mappings

Qiaoyan Bi, Junxiang Xu

• In this paper we consider a class of nearly integrable symplectic mappings with generating function and prove the persistence of lower dimensional hyperbolic invariant tori. Under a Rüssmann-type non-degenerate condition, by using the KAM theory, we proved that the nearly integrable twist symplectic mappings admit a family of lower dimensional invariant tori as long as the generating function is real analytic and the perturbation is sufficiently small.