• Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy 

      Han, Yuecai; Li, Yong; Yi, Yingfei (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 ...
    • Persistence of Hyperbolic Tori in Hamiltonian Systems 

      Li, Yong; Yi, Yingfei (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 ...
    • Persistence of Lower Dimensional Tori of General Types in Hamiltonian Systems 

      Li, Yong; Yi, Yingfei (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 ...
    • A Quasi-Periodic Poincaré's Theorem 

      Li, Yong; Yi, Yingfei (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 ...