arXiv Analytics

Sign in

arXiv:2406.19252 [math.MG]AbstractReferencesReviewsResources

Critical exponents and dimension for generalised limit sets

Tianyi Feng, Jonathan M. Fraser

Published 2024-06-27Version 1

There is a beautiful and well-studied relationship between the Poincare exponent and the fractal dimensions of the limit set of a Kleinian group. Motivated by this, given an arbitrary discrete subset of the unit ball we define a critical exponent and investigate how it relates to the fractal dimensions of the associated generalised limit set.

Comments: 16 pages
Categories: math.MG, math.DS
Related articles: Most relevant | Search more
arXiv:2105.11764 [math.MG] (Published 2021-05-25)
Continuity of critical exponent of quasiconvex-cocompact groups under Gromov-Hausdorff convergence
arXiv:1704.06541 [math.MG] (Published 2017-04-21)
Critical exponent for geodesic currents
arXiv:2110.01881 [math.MG] (Published 2021-10-05, updated 2022-12-10)
Fractal dimensions in the Gromov--Hausdorff space

Links

Toolbox