Geometry, Topology and Dynamics Seminar
Katrin Gelfert
Northwestern University
Expansive Markov systems: geometrical and dynamical properties
Abstract: A well-known result by Cantwell and Conlon states that a Markov exceptional minimal set of a $C^2$ foliation has zero Lebesgue measure.
Starting from this observation we investigate further dynamical properties of Markov systems.
Under an additional assumption of expansivity we are able to describe the Hausdorff dimension
of the minimal set in terms of various dynamical quantifiers: pressure, conformal measures, hyperbolic measures.
In the case of a piecewise analytic system we show that the Hausdorff dimension is strictly less than the dimension of the ambient manifold.
There are also examples showing that a similar result is in general not true for $C^\infty$ systems.
Monday March 10, 2008 at 3:00 PM in SEO 612