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Jose F. Alves

  1. Strong stochastic stability for non-uniformly expanding maps.

    Mon, 03/01/2010 - 16:01 — SomNambul
    Authors: Jose F. Alves, Helder Vilarinho
    Subjects: Dynamical Systems
    Abstract

    We consider random perturbations of discrete-time dynamical systems. We give
    sufficient conditions for the stochastic stability of certain classes of maps,
    in a strong sense. This improves the main result in J. F. Alves, V.

  2. Geometry of expanding absolutely continuous invariant measures and the liftability problem.

    Fri, 10/16/2009 - 04:10 — SomNambul
    Authors: Jose F. Alves, Stefano Luzzatto, Carla L. Dias
    Subjects: Dynamical Systems
    Abstract

    We consider a quite broad class of maps on compact manifolds of arbitrary
    dimension possibly admitting critical points,discontinuities and singularities.
    Under some mild nondegeneracy assumptions we show that (f) admits an induced
    Gibbs-Markov map with integrable inducing times if and only if it has an
    ergodic invariant probability measure which is absolutely continuous with
    respect to the Riemannian volume and has all Lyapunov exponents positive.

  3. Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Jose F. Alves, Vilton Pinheiro
    Subjects: Dynamical Systems
    Abstract

    We consider a partially hyperbolic set $K$ on a Riemannian manifold $M$ whose
    tangent space splits as $T_K M=E^{cu}\oplus E^{s}$, for which the
    centre-unstable direction $E^{cu}$ expands non-uniformly on some local unstable
    disk. We show that under these assumptions $f$ induces a Gibbs-Markov
    structure. Moreover, the decay of the return time function can be controlled in
    terms of the time typical points need to achieve some uniform expanding
    behavior in the centre-unstable direction.

  4. Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Jose F. Alves, Vilton Pinheiro
    Subjects: Dynamical Systems
    Abstract

    We consider a partially hyperbolic set $K$ on a Riemannian manifold $M$ whose
    tangent space splits as $T_K M=E^{cu}\oplus E^{s}$, for which the
    centre-unstable direction $E^{cu}$ expands non-uniformly on some local unstable
    disk. We show that under these assumptions $f$ induces a Gibbs-Markov
    structure. Moreover, the decay of the return time function can be controlled in
    terms of the time typical points need to achieve some uniform expanding
    behavior in the centre-unstable direction.

Math-arch

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