| 概要 | We show that some results on normal subgroups of Kleinian groups have their
natural home in the thermodynamic formalism of Markov shifts with a
countable state space. This includes a result of Brooks which states under
certain conditions, that for a normal subgroup N of Kleinian group G, we
have that \delta(N)=\delta(G) if and only if G/N is amenable, where \delta
refers to the exponent of convergence of the associated Poincare series.
Another result, which is due to Falk and Stratmann and to Roblin, shows
that \delta(N) is bounded below by half of \delta(G) and that this
inequality is strict whenever N is of divergence type. We give a short new
proof of this result. |