Browsing by Subject "KAM theory"
Now showing items 113 of 13

Degenerate Lower Dimensional Tori in Hamiltonian Systems
(Georgia Institute of Technology, 2005) 
An extension of KAM theory to quasiperiodic breather solutions in Hamiltonian lattice systems
(Georgia Institute of Technology, 20071114)We prove the existence and linear stability of quasiperiodic breather solutions in a 1d Hamiltonian lattice of identical, weaklycoupled, anharmonic oscillators with general onsite potentials and under the effect of ... 
Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy
(Georgia Institute of Technology, 2009)We study the existence of quasiperiodic, 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
(Georgia Institute of Technology, 2006)We consider Hamiltonian networks of long ranged and weakly coupled oscillators with variable frequencies. 
On PoincaréTreshchev Tori in Hamiltonian Systems
(Georgia Institute of Technology, 2003)We study the persistence of PoincaréTreshchev tori on a resonant surface of a nearly integrable Hamiltonian system in which the unperturbed Hamiltonian needs not satisfy the Kolmogorov nondegenerate condition. The ... 
Persistence of Hyperbolic Tori in Hamiltonian Systems
(Georgia Institute of Technology, 1999)We generalize the wellknown result of Graff and Zehnder on the persistence of hyperbolic invariant tori in Hamiltonian systems by considering nonFloquet, frequency varying normal forms and allowing the degeneracy of the ... 
Persistence of Invariant Tori on Submanifolds in Hamiltonian Systems
(Georgia Institute of Technology, 1999)Generalizing the degenerate KAM theorem under the Rüssmann nondegeneracy and the isoenergetic KAM theorem, we employ a quasilinear iterative scheme to study the persistence and frequency preservation of invariant tori ... 
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 ... 
QuasiPeriodic Breathers in Hamiltonian Networks of LongRange Coupling
(Georgia Institute of Technology, 20070703)This work is concerned with Hamiltonian networks of weakly and longrange coupled oscillators with either variable or constant onsite frequencies. We derive an infinite dimensional KAMlike theorem by which we establish ... 
A QuasiPeriodic 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 nondegenerate condition. By introducing a quasilinear iterative scheme to deal with ... 
QuasiPeriodic Solutions in a Nonlinear Schrödinger Equation
(Georgia Institute of Technology, 2005)In this paper, onedimensional (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 BoseEinstein Condensates in Periodic Lattices and Superlattices
(Georgia Institute of Technology, 20050723)We employ KAM theory to rigorously investigate the transition between quasiperiodic and chaotic dynamics in cigarshaped BoseEinstein 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
(Georgia Institute of Technology, 20050121)The subject of this paper is twoquasiperiodicity in a large class of oneandahalf degree of freedom Hamiltonian systems. The main result is that such systems have invariant tori for any internal frequency that is of ...