The Persistence Of Lower Dimensional Invariant Tori For Hamiltonian Systems Under Weaker Non-resonance Conditions

In this thesis,we discuss the persistence of lower dimensional hyperbolic invariant tori for Hamiltonian systems under weaker non-resonance conditions.By the method of rational approximation,we will prove that if the frequency mapping satisfies weaker Bruno-Russmann conditions,the invariant tori of the real-analytic non-degenerate integrable Hamiltonian systems will persist under small perturbations.