Journal of Dynamical and Control Systems

, Volume 1, Issue 3, pp 427–445 | Cite as

Fuchsian groups from the dynamical viewpoint

  • A. N. Starkov
Article

Abstract

Here we survey the results on the structure of Fuchsian groups due to Hopf, Hedlund, Sullivan, Nicholls, Pommerenke, and others from the viewpoint of the dynamics of the geodesic and horocycle flows on the corresponding surfaces. Special attention is given to the structure of horocycle orbits; in particular, we construct Fuchsian groups with new types of horocycle orbits which are neither closed nor dense in the nonwandering set. We give a unique classification of Fuchsian groups from the dynamical viewpoint and indicate some open problems.

1991 Mathematics Subject Classification

28D 20H10 

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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. N. Starkov
    • 1
    • 2
  1. 1.All-Russian Electrotechnical InstituteIstra, Moscow regionRussia
  2. 2.Department of MathematicsMoscow State UniversityMoscowRussia

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