Titlebook: Geodesic and Horocyclic Trajectories; Françoise Dal’Bo Textbook 2011 Springer-Verlag London Limited 2011 Fuchsian group.Poincaré half plan

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Topological dynamics of the horocycle flow,he quotient of ..ℍ by the Fuchsian group corresponding to .. In the geometrically finite case, we show that the horocycle flow is less topologically turbulent than the geodesic flow (Sect. 4)..Throughout this chapter, we use the definitions and notations associated with the dynamics of a flow as originally introduced in Appendix A.

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Textbook 2011nces 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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https://doi.org/10.1007/978-3-662-28982-2es of ..(...) in terms of sequences. As applications, we will construct, in the general case of a non-elementary Fuchsian group .′, trajectories of the geodesic flow on . which are neither periodic nor dense.

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担忧

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Topological dynamics of the horocycle flow,ur method is based on a correspondence between the set of horocycles of ℍ and the space of non-zero vectors in ℝ. modulo {±Id}. This vectorial point of view allows one to relate the topological dynamics of the linear action on ℝ. of a discrete subgroup . of SL(2,ℝ) to that of the horocycle flow on t

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The Lorentzian point of view, group associated with . on {±Id}ℝ.−{0}..Our motivation in this chapter, is to construct a linear representation of . taking into account simultaneously the dynamics of the horocycle and of the geodesic flows. Many proofs are reformulations of proofs given in the previous chapters. In this case, the