EVENT DETAILS AND ABSTRACT

Title: Multifractal analysis in nonuniformly hyperbolic dynamics
Speaker: Professor Katrin Gelfert
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

Given a smooth dynamical system, we study level sets of Lyapunov regular points with equal exponent. Possible measures for the "complexity" of such level sets are their Hausdorff dimension or their topological entropy (i.e. the entropy of the dynamical system restricted to it). If the dynamics is not uniformly hyperbolic, then the set of points with zero Lyapunov exponent can be considered to be quite large or small (when measured e.g. in terms of dimension and entropy). This is investigated by means of the thermodynamic formalism for sub-systems which are uniformly hyperbolic. Such a scheme can be succesfully applied to primary examples of conformal dynamics such as parabolic interval maps and rational maps on the Riemann sphere. But principle techniques also extend to surface diffeomorphisms and certain flows in 3-dimensional manifolds.