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On Almost Automorphic Dynamics in Symbolic Lattices
(Georgia Institute of Technology, 2002)
We study the existence, structure, and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular we show that almost automorphic arrays with arbitrarily large entropy are typical ...
Quasiperiodic and Chaotic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices
(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 ...
Center Manifolds for Invariant Sets
(Georgia Institute of Technology, 1999)
We derive a general center manifolds theory for a class of compact invariant sets of flows generated by a smooth vector fields in R^n. By applying the Hadamard graph transform technique, it is shown that, associated to ...
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 ...
A Local Variational Principle of Pressure and Its Applications to Equilibrium States
(Georgia Institute of Technology, 2004)
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 ...
Nekhoroshev and Kam Stabilities in Generalized Hamiltonian Systems
(Georgia Institute of Technology, 2003)
We present some Nekhoroshev stability results for nearly integrable, generalized Hamiltonian systems which can be odd dimensional and admit a distinct number of action and angle variables. Using a simultaneous approximation ...
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 ...
Persistence of Invariant Tori in Generalized Hamiltonian Systems
(Georgia Institute of Technology, 2001)
We present some results of KAM type, comparable to the KAM theory for volume-preserving maps and flows, for generalized Hamiltonian systems which may admit a distinct number of action and angle variables. In particular, ...