Stratmann, Bernd O.Zielicz, AnnaAnnaZielicz2020-03-092020-03-092015-05-29https://media.suub.uni-bremen.de/handle/elib/867We introduce and study the class of geometric Schottky groups which includes many infinitely generated groups. We define a natural coding of the limit set and characterise in terms of this coding important subsets of the limit set. Further, we study a certain notion of entropy for the geodesic flow on the quotient manifold. We show that for geometric Schottky groups it is equal to the convex core entropy of the group, which for finitely generated groups agrees with the Poincar'e exponent. Subsequently, we discuss a subclass of the geometric Schottky groups called the P-class. For groups in this class, the geodesic flow is ergodic with respect to the Liouville-Patterson measure and the Liouville-Patterson measure is finite. We present proofs of these facts and deduce some consequences. Lastly, we provide methods of constructing groups in the P-class and then show that an infinite-index normal subgroup of a finitely generated geometric Schottky group cannot belong to the P-class.enBitte wählen Sie eine Lizenz aus: (Unsere Empfehlung: CC-BY)hyperbolic geometrygeometic Schottky groupFuchsian groupKleinian groupSchottky grouplimit setgeodesic flowentropyBowen-Dinaburg entropyPoincar'e exponentexponent of convergenceconvex core entropyLiouville-Patterson measurePatterson measureSullivanshadow lemmaergodicP-classreverse triangle inequality510Dissertationurn:nbn:de:gbv:46-00104579-13