Dynamics of Fuchsian groups

  • Françoise Dal’Bo
Part of the Universitext book series (UTX)


This chapter is an introduction to the planar hyperbolic geometry. There are many books which cover it. Our text is inspired by three of them: A. Beardon’s “The geometry of discrete groups” Springer, New York 1995, A. Katok’s and V. Climenhaga’s “Lectures on Surfaces” American Mathematical Society, Providence 2008, and S. Katok’s “Fuchsian groups” University of Chicago Press, Chicago 1992. The reader will find in these books the solutions of the exercises suggested in this chapter.

We assume that the reader has some background in complex analysis and differential geometry. For a short introduction to Riemannian geometry, see Appendix B.

Sections 3 and 4 do not include many examples. Readers who prefer to see examples of Fuchsian groups before studying their properties are invited to browse through Chap. II.


Fuchsian Group Perpendicular Bisector Parabolic Point Hyperbolic Length Hyperbolic Isometry 
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  1. [7]
    Beardon, A.F.: The Geometry of Discrete Groups. Graduate Texts in Math., vol. 91. Springer, New York (1995), pp. 337 Google Scholar
  2. [39]
    Katok, A., Climenhaga, V.: Lectures on Surfaces. Student Mathematical Library, vol. 46. American Mathematical Society, Providence (2008), pp. 286 Google Scholar
  3. [41]
    Katok, S.: Fuchsian Groups. Chicago Lectures in Mathematics. University of Chicago Press, Chicago (1992), pp. 175 Google Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.IRMARUniversité Rennes 1Rennes CedexFrance

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