On Poincaré-Treshchev Tori in Hamiltonian Systems

1991 Mathematics Subject Classifi cation. 58F14, 58F05, 58F30, 37J40.We study the persistence of Poincaré-Treshchev tori on a resonant surface of a nearly integrable Hamiltonian system in which the unperturbed Hamiltonian needs not satisfy the Kolmogorov non-degenerate condition. The persistence of the majority of invariant tori associated to g-nondegenerate relative equilibria on the resonant surface will be shown under a Rüssmann like condition.The rst author is partially supported by NSFC 19971042, National 973 Key Project of China: Nonlinearity, and National outstanding young's award of China. The second author was partially supported by NSF grant DMS0204119