Relative Growth in Hyperbolic Groups

Relative Growth Series in some Hyperbolic Groups

We study certain groups of isometries of hyperbolic space (including certain hyperbolic Coxeter groups) and normal subgroups with quotient Zν , ν ≥ 1. We show that the associated relative growth series are not rational. This extends results obtained by Grigorchuk and de la Harpe for free groups and Pollicott and the author for surface groups.

RELATIVE GROWTH SERIES IN SOME HYPERBOLIC GROUPSRichard

Growth of relatively hyperbolic groups

We show that a relatively hyperbolic group either is virtually cyclic or has uniform exponential growth. Mathematics Subject Classification(2000). 20F65.

Relative Hyperbolic Extensions of Groups and Cannon-thurston Maps

Let 1 → (K, K1) → (G, NG(K1)) → (Q, Q1) → 1 be a short exact sequence of pairs of finitely generated groups with K strongly hyperbolic relative to the subgroup K1. Let relative hyperbolic boundary of K with respect to K1 contains atleast three distinct parabolic end points and for all g ∈ G there exists k ∈ K such that gK1g −1 = kK1k , then we prove that there exists a quasi-isometric section s...

Relative Entropy in Hyperbolic Relaxation

We provide a framework so that hyperbolic relaxation systems are endowed with a relative entropy identity. This allows a direct proof of convergence in the regime that the limiting solution is smooth.