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Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy
(Georgia Institute of Technology, 2009)
We study the existence of quasi-periodic, invariant tori in a nearly integrable Hamiltonian system of high order proper degeneracy, i.e., the integrable part of the Hamiltonian involves several time scales and at each time ...
A Quasi-Periodic Poincaré's Theorem
(Georgia Institute of Technology, 1999)
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 ...
Persistence of Lower Dimensional Tori of General Types in Hamiltonian Systems
(Georgia Institute of Technology, 1999)
The work is a generalization to [40] in which we study the persistence of lower dimensional tori of general type in Hamiltonian systems of general normal forms. By introducing a modified linear KAM iterative scheme to deal ...
Persistence of Hyperbolic Tori in Hamiltonian Systems
(Georgia Institute of Technology, 1999)
We generalize the well-known result of Graff and Zehnder on the persistence of hyperbolic invariant tori in Hamiltonian systems by considering non-Floquet, frequency varying normal forms and allowing the degeneracy of
the ...