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Aaron W. Brown

  1. Rigid properties of measures on the torus: smooth stabilizers and entropy.

    Пт, 08/20/2010 - 15:01 — SomNambul
    Authors: Aaron W. Brown
    Subjects: Dynamical Systems
    Abstract

    For a nonlinear Anosov diffeomorphism $a$ of the 2-torus, we present examples
    of equilibrium states $\mu$ such that the group of $\mu$-preserving
    diffeomorphism is virtually cyclic. We then present a larger class of
    $a$-invariant measures for which the set of entropies for all $C^{1+\alpha}$
    diffeomorphisms is a semi-group isomorphic $\N$.

  2. Nonexpanding Attractors: Conjugacy to Algebraic Models and Classification in 3-Manifolds.

    Пнд, 05/10/2010 - 15:01 — SomNambul
    Authors: Aaron W. Brown
    Subjects: Dynamical Systems
    Abstract

    We prove a result motivated by Williams's classification of expanding
    attractors and the Franks-Newhouse Theorem on codimension-1 Anosov
    diffeomorphisms: If a mixing hyperbolic attractor has 1-dimensional unstable
    manifolds then it is either is expanding or is homeomorphic to a compact
    abelian group (a toral solenoid); in the latter case the dynamics is conjugate
    to a group automorphism. As a corollary we obtain a classification of all
    2-dimensional basic sets in 3-manifolds.

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