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Chow, Shui-Nee

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Now showing 1 - 6 of 6
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    Persistence of Invariant Tori on Submanifolds in Hamiltonian Systems
    (Georgia Institute of Technology, 1999) Chow, Shui-Nee ; Li, Yong ; Yi, Yingfei
    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 on a smooth sub-manifold for a real analytic, nearly integrable Hamiltonian system. Under a nondegenerate condition of Rüssmann type on the sub-manifold, we shall show the following: a) the majority of the unperturbed tori on the sub-manifold will persist; b) the perturbed toral frequencies can be partially preserved according to the maximal degeneracy of the Hessian of the unperturbed system and be fully preserved if the Hessian is nondegenerate; c) the Hamiltonian admits normal forms near the perturbed tori of arbitrarily prescribed high order. Under a sub-isoenergetic nondegenerate condition on an energy surface, we shall show that the majority of unperturbed tori give rise to invariant tori of the perturbed system of the same energy which preserve the ratio of certain components of the respective frequencies.
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    Center Manifolds for Invariant Sets
    (Georgia Institute of Technology, 1999) Chow, Shui-Nee ; Liu, Weishi ; Yi, Yingfei
    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 certain dynamical characteristics of the linearized flow along the invariant set, there exists an invariant manifold (called a center manifold) of the invariant set which contains every locally bounded solution (in particular, contains the invariant set) and is persistent under small perturbations.
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    Center Manifolds for Invariant Manifolds
    (Georgia Institute of Technology, 1997) Chow, Shui-Nee ; Liu, Weishi ; Yi, Yingfei
    We study dynamics of flows generated from smooth vector fields in R^n in the vicinity of an invariant and closed smooth manifold Y. By applying the Hadamard graph transform technique, we show that there exists an invariant manifold (called a center manifold of Y) based on the information of the linearization along Y, which contains every locally bounded solution and is persistent under small perturbations.
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    Stability and Bifurcation of Traveling Wave Solutions in Coupled Map Lattices
    (Georgia Institute of Technology, 1994) Chow, Shui-Nee ; Shen, Wenxian
    A class of coupled map lattices are considered. For each such coupled map lattice, the stability and bifurcation of its traveling wave solutions are studied. A stability criteria is given. It is shown that bifurcation scenario in coupled map lattices is similar to but different from that arising in reaction diffusion equations. As an application of the general results, the dynamics near traveling wave solutions in a discrete Huxley equation is discussed.
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    Dynamics in a Discrete Nagumo Equation - Spatial Topological Chaos
    (Georgia Institute of Technology, 1994) Chow, Shui-Nee ; Shen, Wenxian
    In this paper we show the existence of spatial topological chaos in a discrete Nagumo equation, and discuss the similarities and differences between the discrete Nagumao equation and the continuous one.
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    Dynamical systems and applications
    (Georgia Institute of Technology, 1994) Chow, Shui-Nee