DATE:     5/2
TIME:     1:10, Weber 223
SPEAKER:  Sjoerd Verduyn Lunel (Mathematisch Instituut, Universiteit Leiden)
TITLE:    Calculating Hausdorff dimensions of invariant sets using
          spectral theory

ABSTRACT:  The dimension of an invariant set of a dynamical system is
one of the most important characteristics. In this talk we
present a new approach to compute the Hausdorff dimension of
conformally self-similar invariant sets. The approach is based
on a direct spectral analysis of the transfer operator associated
with the dynamical system. In the case that the maps defining the
dynamical system are analytic, our method yields a sequence of
successive approximations that converge to the Hausdorff dimension
of the invariant set at a super-exponential rate. This allows us
to estimate the dimension very precisely. We illustrate our
approach with examples from dynamical systems and from number
theory via Diophantine approximations.