Mobius transformations and the related inequalities

Abstract

The aim is to study the M¨obius transformations and the various norms related to it. These norms are defined by using three parameters which are invariant under conjugation. Using these parameters we define a two generator group. We then derive analogous results when this group is an arbitrary discrete subgroup of M. Lastly, continued fractions is studied by examining action of M¨obius maps in hyperbolic space as continued fractions can be regarded as sequence of M¨obius maps.