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Topological quasi-stability of partially hyperbolic diffeomorphisms under random perturbations

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  • In this paper, $C^0$ random perturbations of a partially hyperbolic diffeomorphism are considered. It is shown that a partially hyperbolic diffeomorphism is quasi-stable under such perturbations.
    Mathematics Subject Classification: Primary: 37D20; Secondary: 37H99.


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  • [1]

    L. Arnold, "Random Dynamical Systems," Springer Monographs in Mathematics, Springer-Verlag, New York, 1998.


    M. Brin and Ya. Pesin, Partially hyperbolic dynamical systems, Math. USSR-Izv., 8 (1974), 177-218.doi: 10.1070/IM1974v008n01ABEH002101.


    A. Fathi, M. Herman and J. Yoccoz, A proof of Pesin's stable manifold theorem, in "Geometric Dynamics," Lect. Notes in Math., 1007, Springer-Verlag, Berlin-Heidelberg, (1983), 177-215.doi: 10.1007/BFb0061417.


    M. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Bull. Amer. Math. Soc., 76 (1970), 1015-1019.doi: 10.1090/S0002-9904-1970-12537-X.


    M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," Lect. Notes in Math., 583, Springer-Verlag, Berlin-New York, 1977.


    H. Hu and Y. ZhuQuasi-stability of partially hyperbolic diffeomorphisms, to appear in Tran. Amer. Math. Soc., arXiv:1210.4766.


    Y. Kifer, "Random Perturbations of Dynamical Systems," Progress in Probability and Statistics, 16, Birkhäuser Boston, Inc., Boston, MA, 1988.doi: 10.1007/978-1-4615-8181-9.


    P.-D. Liu, Dynamics of random transformations: Smooth ergodic theory, Ergo. Theo. Dyn. Syst., 21 (2001), 1279-1319.doi: 10.1017/S0143385701001614.


    P.-D. Liu, Random perturbations of Axiom A basic sets, J. Stat. Phys., 90 (1998), 467-490.doi: 10.1023/A:1023280407906.


    P.-D. Liu and M. Qian, "Smooth Ergodic Theory of Random Dynamical Systems," Lect. Notes in Math., 1606, Springer-Verlag, Berlin, 1995.


    Q. X. Liu and P. D. Liu, Topological stability of hyperbolic sets of flows under random perturbations, Discrete Contin. Dyn. Syst. Ser. B, 13 (2010), 117-127.doi: 10.3934/dcdsb.2010.13.117.


    Ya. Pesin, "Lectures on Partial Hyperbolicity and Stable Ergodicity," Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2004.doi: 10.4171/003.


    P. Walters, Anosov diffeomorphisms are topologically stable, Topology, 9 (1970), 71-78.doi: 10.1016/0040-9383(70)90051-0.


    Y. Zhu, J. Zhang and L. He, Shadowing and inverse shadowing for $C^1$ endomorphisms, Acta Mathematica Sinica (Engl. Ser.), 22 (2006), 1321-1328.doi: 10.1007/s10114-005-0739-6.

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