Groups, Geometry, and Dynamics

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Volume 11, Issue 4, 2017, pp. 1497–1519
DOI: 10.4171/GGD/436

Published online: 2017-12-07

Critical points for the Hausdorff dimension of pairs of pants

Mark Pollicott[1] and Polina Vytnova[2]

(1) University of Warwick, Coventry, UK
(2) Queen Mary University of London, UK

We study the dependence of the Hausdorff dimension of the limit set of a hyperbolic Fuchsian group on the geometry of the associated Riemann surface. In particular, we study the type and location of extrema subject to restriction on the total length of the boundary geodesics. In addition, we compare different algorithms used for numerical computations.

Keywords: Closed geodesics, Hausdorff dimension, Fuchsian group, limit set, numerical estimates, Riemann surface, Selberg zeta function

Pollicott Mark, Vytnova Polina: Critical points for the Hausdorff dimension of pairs of pants. Groups Geom. Dyn. 11 (2017), 1497-1519. doi: 10.4171/GGD/436