On some exotic Schottky groups

Abstract

We construct a Cartan-Hadamard manifold with pinched negative curvature whose group of isometries possesses divergent discrete free subgroups with parabolic elements who do not satisfy the so-called "parabolic gap condition" . This construction relies on the comparaison between the Poincar\'e series of these free groups and the potential of some transfer operator which appears naturally in this context.