Time: 2018.01.16, 15:15–17:00
Location: Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Critical exponents for normal subgroups."
Speaker: Rhiannon Dougall (Université de Nantes)
Abstract: Fix a cocompact group $$\Gamma_0$$ of isometries of a negatively curved, simply connected manifold $$X$$. We are interested in the dynamics of its normal subgroups $$\Gamma$$. Namely, we study the critical exponent $$\delta_\Gamma$$, which is the exponential growth rate of the $$\Gamma$$–orbit of a point. We characterise the existence of a gap $$\delta_\Gamma<\delta_{\Gamma_0}$$ uniform in a family of normal subgroups $$\Gamma$$, in terms of permutation representations given by the quotients $$\Gamma_0/\Gamma$$. The proof uses the symbolic dynamics for the geodesic flow, for which we obtain the analogous statements for countable state shifts obtained as group extensions of a finite state shift.