Now showing items 1-13 of 13

    • Degenerate Lower Dimensional Tori in Hamiltonian Systems 

      Han, Yuecai; Li, Yong; Yi, Yingfei (Georgia Institute of Technology, 2005)
    • An extension of KAM theory to quasi-periodic breather solutions in Hamiltonian lattice systems 

      Viveros Rogel, Jorge (Georgia Institute of Technology, 2007-11-14)
      We prove the existence and linear stability of quasi-periodic breather solutions in a 1d Hamiltonian lattice of identical, weakly-coupled, anharmonic oscillators with general on-site potentials and under the effect of ...
    • 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 ...
    • A KAM Theorem for Hamiltonian Networks with Long Ranged Couplings 

      Geng, Jiansheng; Yi, Yingfei (Georgia Institute of Technology, 2006)
      We consider Hamiltonian networks of long ranged and weakly coupled oscillators with variable frequencies.
    • 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 ...
    • Quasi-Periodic Breathers in Hamiltonian Networks of Long-Range Coupling 

      Geng, Jiansheng; Viveros, Jorge; Yi, Yingfei (Georgia Institute of Technology, 2007-07-03)
      This work is concerned with Hamiltonian networks of weakly and long-range coupled oscillators with either variable or constant on-site frequencies. We derive an infinite dimensional KAM-like theorem by which we establish ...
    • 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 ...
    • Quasiperiodic and Chaotic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices 

      van Noort, Martijn; Porter, Mason; Yi, Yingfei; Chow, Shui-Nee (Georgia Institute of Technology, 2005-07-23)
      We employ KAM theory to rigorously investigate the transition between quasiperiodic and chaotic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a ...
    • Quasiperiodic Dynamics in Hamiltonian 1 1/2 Degree of Freedom Systems Far from Integrability 

      Chow, Shui-Nee; van Noort, Martijn; Yi, Yingfei (Georgia Institute of Technology, 2005-01-21)
      The subject of this paper is two-quasiperiodicity in a large class of one-and-a-half degree of freedom Hamiltonian systems. The main result is that such systems have invariant tori for any internal frequency that is of ...