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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.21 n.1 Antofagasta mayo 2002

http://dx.doi.org/10.4067/S0716-09172002000100006 

Proyecciones
Vol. 21, N o 1, pp. 97-108, May 2002.
Universidad Católica del Norte
Antofagasta - Chile

ON THE VOLUMETRIC ENTROPY
IN THE NON COMPACT CASE

 

ANDRÉS NAVAS
École Normale Supérieure de Lyon, France

 

Abstract

We give an example of a non compact riemannian manifold with finite volume for which the limit corresponding to the clas-sical definition of the volumetric entropy does not exist. This confirms the fact that in the non compact finite volume case,the natural definition is given by the critical exponent of the mean growth rate for the volume on the riemannian covering.

Subject classification AMS 2000 : Primary 37A35 ; Secondary : 37D40, 53C24.

Keywords : Entropy, volume growth.

 

References

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[Gr] M.Gromov. Volume and bounded cohomology. Publ. Math IHES 56, (1981), pp.213-307.         [ Links ]

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Received : January, 2002.

Andrés Navas
Unité de Mathématiques Pures et Appliquées,
École Normale Supérieure de Lyon
UMR 5669 du CNRS
46 allée d’Italie
F-69364 Lyon 07
France
e-mail: anavas@umpa.ens-lyon.fr

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