Fuchsian groups from the dynamical viewpoint
This paper provides an elementary introduction to Fuchsian groups theory for specialists on dynamical systems. The author paid special attention to the structure of orbits of the horocycle flow on \(T^1M\) of the corresponding hyperbolic surface \(M=\Gamma\setminus\Delta\), where \(\Gamma\) is the Fuchsian group. He constructs Fuchsian groups with new types of horocycle orbits which are neither closed nor dense in the nonwandering set. Moreover, the author presents both a unique classification of Fuchsian groups from the dynamical point of view and some open problems.
scientific article; zbMATH DE number 1431794