Softcover ISBN:  9782856299012 
Product Code:  SMFMEM/160 
List Price:  $52.00 
AMS Member Price:  $41.60 
Softcover ISBN:  9782856299012 
Product Code:  SMFMEM/160 
List Price:  $52.00 
AMS Member Price:  $41.60 

Book DetailsMémoires de la Société Mathématique de FranceVolume: 160; 2019; 132 ppMSC: Primary 20
Let \(M=X/\Gamma\) be a geometrically finite negatively curved manifold with fundamental group \(\Gamma\) acting on X by isometries. The purpose of this book is to study the mixing property of the geodesic flow on \(\mathrm{T}^{1}\mathrm{M}\), the asymptotic behavior as \(R\rightarrow+\infty\) of the number of closed geodesics on M of length less than \(R\) and of the orbital counting function \(\sharp\{\gamma\in\Gamma\vert d(\mathbf{o},\gamma\cdot \mathbf{o})\le R\}\).
These properties are well known when the BowenMargulis measure on \(\mathrm{T}^{1}\mathrm{M}\) is finite. The author considers here Schottky group \(\Gamma=\Gamma_{1}\ast\Gamma_{2}\ast\cdots\ast\Gamma_{k}\) whose BowenMargulis measure is infinite and ergodic, such that one of the elementary factor \(\Gamma_{i}\) is parabolic with \(\delta_{\Gamma_{i}}=\delta_{\Gamma}\).
The author specifies these ergodic properties using a symbolic coding induced by the Schottky group structure.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.

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Let \(M=X/\Gamma\) be a geometrically finite negatively curved manifold with fundamental group \(\Gamma\) acting on X by isometries. The purpose of this book is to study the mixing property of the geodesic flow on \(\mathrm{T}^{1}\mathrm{M}\), the asymptotic behavior as \(R\rightarrow+\infty\) of the number of closed geodesics on M of length less than \(R\) and of the orbital counting function \(\sharp\{\gamma\in\Gamma\vert d(\mathbf{o},\gamma\cdot \mathbf{o})\le R\}\).
These properties are well known when the BowenMargulis measure on \(\mathrm{T}^{1}\mathrm{M}\) is finite. The author considers here Schottky group \(\Gamma=\Gamma_{1}\ast\Gamma_{2}\ast\cdots\ast\Gamma_{k}\) whose BowenMargulis measure is infinite and ergodic, such that one of the elementary factor \(\Gamma_{i}\) is parabolic with \(\delta_{\Gamma_{i}}=\delta_{\Gamma}\).
The author specifies these ergodic properties using a symbolic coding induced by the Schottky group structure.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.