Tuesday, February 9, 2010

Non-uniformly hyperbolic structures

Katrin G. Gelfert

Abstract: I will discuss some approaches to study dynamical systems that lack uniform hyperbolic behavior. Such approaches can be used, for example, to study level sets of points that are Lyapunov regular and have equal exponent. If the dynamical system is not uniformly hyperbolic, then the set of points with a small or zero Lyapunov exponent can be quite large or small (when measured e.g. in terms of fractal dimension or topological entropy). This is investigated by means of the thermodynamic formalism and a certain family of uniformly hyperbolic sub-systems that `exhaust' the non-uniformy hyperbolic system. Our scheme can be succesfully applied to primary examples of conformal dynamics such as parabolic or unimodal interval maps and rational maps on the Riemann sphere. However, principle techniques also extend to surface diffeomorphisms and certain flows in 3-dimensional manifolds.

Tuesday, February 9, 2010
Time: 11h30
Room: B1-01, Complexo Interdisciplinar, UL