Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces.
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Cambridge University Press, Buser, Geometry and spectra of compact Riemann surfaces. Birkhauser, Dal'Bo, Geodesic and horocyclic trajectories. Universitext, Einsiedler and E.
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Lindenstrauss, Diagonal actions on locally homogeneous spaces. Clay Math.
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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. Help Centre. My Wishlist Sign In Join. Be the first to write a review. Add to Wishlist. Ships in 15 business days. Link Either by signing into your account or linking your membership details before your order is placed.
Geodesic and Horocyclic Trajectories (Universitext)
The first family of groups that we will consider consists of geometrically finite free groups, called Schottky groups. Its construction is based on the dynamics of isometries. The second family comes from number theory. We will study each of these groups according the same general outline: description of a fundamental domain;. We will also construct a coding of the limit sets of Schottky groups and of the modular group.
We will use this coding in Chap.
Geodesic and Horocyclic Trajectories
IV to study the dynamics of the geodesic flow, and in Chap. VII to translate the behavior of geodesic rays on the modular surface into the terms of Diophantine approximations.
Our motivation is to give relations between the behavior of this flow and the nature of the points in the limit set of the group. The possible cases are diagrammed below in Fig.
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For further details, the reader may refer to Sect.