\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Topological conjugacies and behavior at infinity

Abstract Related Papers Cited by
  • We obtain a version of the Grobman--Hartman theorem in Banach spaces for perturbations of a nonuniform exponential contraction, both for discrete and continuous time. More precisely, we consider the general case of an exponential contraction with an arbitrary nonuniform part and obtained from a nonautonomous dynamics, and we establish the existence of Hölder continuous conjugacies between an exponential contraction and any sufficiently small perturbation. As a nontrivial application, we describe the asymptotic behavior of the topological conjugacies in terms of the perturbations: namely, we show that for perturbations growing in a certain controlled manner the conjugacies approach zero at infinity and that when the perturbations decay exponentially at infinity the conjugacies have the same exponential behavior.
    Mathematics Subject Classification: Primary: 37D10, 37D25.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    L. Barreira and C. Valls, Stable manifolds for nonautonomous equations without exponential dichotomy, J. Differential Equations, 221 (2006), 58-90.

    [2]

    L. Barreira and C. Valls, Nonuniform exponential dichotomies and Lyapunov regularity, J. Dynam. Differential Equations, 19 (2007), 215-241.

    [3]

    G. Belickiĭ, Functional equations, and conjugacy of local diffeomorphisms of finite smoothness class, Functional Anal. Appl., 7 (1973), 268-277.

    [4]

    G. Belickiĭ, Equivalence and normal forms of germs of smooth mappings, Russian Math. Surveys, 33 (1978), 107-177.

    [5]

    D. Grobman, Homeomorphism of systems of differential equations, Dokl. Akad. Nauk SSSR, 128 (1959), 880-881.

    [6]

    D. Grobman, Topological classification of neighborhoods of a singularity in $n$-space, Mat. Sb. (N.S.), 56 (1962), 77-94.

    [7]

    P. Hartman, A lemma in the theory of structural stability of differential equations, Proc. Amer. Math. Soc., 11 (1960), 610-620.

    [8]

    P. Hartman, On the local linearization of differential equations, Proc. Amer. Math. Soc., 14 (1963), 568-573.

    [9]

    P. McSwiggen, A geometric characterization of smooth linearizability, Michigan Math. J., 43 (1996), 321-335.

    [10]

    J. Palis, On the local structure of hyperbolic points in Banach spaces, An. Acad. Brasil. Ci., 40 (1968), 263-266.

    [11]

    K. Palmer, A generalization of Hartman's linearization theorem, J. Math. Anal. Appl., 41 (1973), 753-758.

    [12]

    C. Pugh, On a theorem of P. Hartman, Amer. J. Math., 91 (1969), 363-367.

    [13]

    G. Sell, Smooth linearization near a fixed point, Amer. J. Math., 107 (1985), 1035-1091.

    [14]

    S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math., 79 (1957), 809-824.

    [15]

    S. Sternberg, On the structure of local homeomorphisms of euclidean $n$-space. II., Amer. J. Math., 80 (1958), 623-631.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(57) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return