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math.GT2021
Pressure metrics for cusped Hitchin components
Harrison Bray, Richard Canary, Lien-Yung Kao +1
We study the cusped Hitchin component consisting of (conjugacy classes of) cusped Hitchin representations of a torsion-free geometrically finite Fuchsian group into PSL(d,R). We pr…
math.DS2021
A global shadow lemma and logarithm law for geometrically finite Hilbert geometries
Harrison Bray, Giulio Tiozzo
For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-…
math.DS2021
Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations
Harrison Bray, Richard Canary, Lien-Yung Kao +1
We show that if an eventually positive, non-arithmetic, locally Hölder continuous potential for a topologically mixing countable Markov shift with (BIP) has an entropy gap at infin…