On McMullen's algorithm for the Hausdorff dimension of Complex Schottky Groups

2021/01/28 by Alejandro Ucan-Puc, Sergio Romaña, Ucan-Puc, Alejandro +1
Mathematics · #20H10 #32M99 Secondary 30F45 #37F99 #57M60 #65Z05 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37M99 #math.DS #msc:20H10 #msc:30F45 #msc:32M99 #msc:37F99 #msc:37M99 #msc:57M60 #msc:65Z05

paper · pdf · doi:10.48550/arxiv.2101.12070

16 pages, 4 figures, 3 algorithm

arxiv created 2021/01/28 · arxiv updated 2021/01/29

Abstract

We provide a generalization of the McMullen's algorithm to approximate the Hausdorff dimension of the limit set for convex-cocompact subgroups of isometries of the Complex Hyperbolic Plane.

Related

• Hausdorff dimension, diverging Schottky representations and the infinite dimensional hyperbolic space
• Some spectral applications of McMullen's Hausdorff dimension algorithm
• Variation of the Hausdorff dimension and degenerations of Schottky groups
• Hausdorff dimension of directional limit sets for self-joinings of hyperbolic manifolds
• The classification of Kleinian groups of Hausdorff dimensions at most one and Burnside's conjecture