Journal
MATHEMATISCHE ANNALEN
Volume 326, Issue 4, Pages 649-690Publisher
SPRINGER-VERLAG
DOI: 10.1007/s00208-002-0399-0
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We study the persistence of invariant tori on resonant surfaces of a nearly integrable Hamiltonian system under the usual Kolmogorov non-degenerate condition. By introducing a quasi-linear iterative scheme to deal with small divisors, we generalize the Poincare theorem on the maximal resonance case (i.e., the periodic case) to the general resonance case (i.e., the quasi-periodic case) by showing the persistence of majority of invariant tori associated to non-degenerate relative equilibria on any resonant surface.
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