Geodesic and Horocyclic Trajectories presents an introduction to
the topological dynamics of two classical flows associated with
surfaces of curvature 1, namely the geodesic and horocycle flows.
Written primarily with the idea of highlighting, in a relatively
elementary framework, the existence of gateways between some
mathematical fields, and the advantages of using them, historical
aspects of this field are not addressed and most of the references
are reserved until the end of each chapter in the Comments section.
Topics within the text cover geometry, and examples, of Fuchsian
groups; topological dynamics of the geodesic flow; Schottky groups;
the Lorentzian point of view and Trajectories and Diophantine
approximations.
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