• Degenerate Lower Dimensional Tori in Hamiltonian Systems 

      Han, Yuecai; Li, Yong; Yi, Yingfei (Georgia Institute of Technology, 2005)
    • On Poincaré-Treshchev Tori in Hamiltonian Systems 

      Li, Yong; Yi, Yingfei (Georgia Institute of Technology, 2003)
      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 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 Invariant Tori on Submanifolds in Hamiltonian Systems 

      Chow, Shui-Nee; Li, Yong; Yi, Yingfei (Georgia Institute of Technology, 1999)
      Generalizing the degenerate KAM theorem under the Rüssmann non-degeneracy and the isoenergetic KAM theorem, we employ a quasi-linear iterative scheme to study the persistence and frequency preservation of invariant tori ...
    • 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 ...
    • Quasi-Periodic Solutions in a Nonlinear Schrödinger Equation 

      Geng, Jiansheng; Yi, Yingfei (Georgia Institute of Technology, 2005)
      In this paper, one-dimensional (1D) nonlinear Schrödinger equation [equation omitted] with the periodic boundary condition is considered. It is proved that for each given constant potential m and each prescribed integer N ...