HOROWITZ SEMINAR

PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS

  • Monday, 16/12/2002, at 14:30 in: room 210, Schreiber Bldg.

  • Hillel Furstenberg (Hebrew U.)

    will speak on

  • The Dimension Conjecture for Commuting Transformations

  • Abstract:

    Let M be a compact manifold or a sequence space with a natural notion of Hausdorff dimension for its subsets. Let T and S be commuting expanding transformations (i.e., nearby points are moved into points more distant from one another). Let x be any point in M, and consider the orbit closures of x under the action of T alone, under S alone, and under the two together. The "dimension conjecture" asserts that the sum of the dimensions of the first two is at least equal to the dimension of the last.

    We will discuss various problems related to this conjecture; particularly for the operators

    Tx = px (mod 1), Sx = qx (mod 1)

    where p and q are not powers of the same integer.

    Some of these involve "nice" fractals and their intersection properties.

    To suggest a talk (yours, or someone elses), contact Jon. Aaronson:
    email

    Back to: Jon Aaronson's homepage.

      Last update on 20/10/02.