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On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition
In this paper we prove the persistence of elliptic lower
dimensional invariant tori for nearly integrable Gevrey-smooth
Hamiltonian systems under Rüssmann's non-degeneracy condition by
an improved KAM iteration, and the persisting invariant tori are
Gevrey smooth with respect to parameters in the sense of Whitney,
with a Gevrey index depending on the Gevrey class of Hamiltonian
systems and on the exponent in the Diophantine condition. Moreover
the Gevrey index should be optimal for the Diophantine condition
in the proof of our theorem.