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Ergodic Properties of Some Negatively Curved Manifolds with Infinite Measure
 
Pierre Vidotto Laboratoire Jean Leray, Nantes, France
A publication of the Société Mathématique de France
Ergodic Properties of Some Negatively Curved Manifolds with Infinite Measure
Softcover ISBN:  978-2-85629-901-2
Product Code:  SMFMEM/160
List Price: $52.00
AMS Member Price: $41.60
Please note AMS points can not be used for this product
Ergodic Properties of Some Negatively Curved Manifolds with Infinite Measure
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Ergodic Properties of Some Negatively Curved Manifolds with Infinite Measure
Pierre Vidotto Laboratoire Jean Leray, Nantes, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-901-2
Product Code:  SMFMEM/160
List Price: $52.00
AMS Member Price: $41.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    Mémoires de la Société Mathématique de France
    Volume: 1602019; 132 pp
    MSC: 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 Bowen-Margulis 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 Bowen-Margulis 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.

    Readership

    Graduate students and research mathematicians.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1602019; 132 pp
MSC: 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 Bowen-Margulis 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 Bowen-Margulis 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.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.