On the volumetric entropy in the non compact case
DOI:
https://doi.org/10.4067/S0716-09172002000100006Keywords:
Entropy, volume growth, entropía, crecimiento de volumen.Abstract
We give an example of a non compact riemannian manifold with finite volume for which the limit corresponding to the classical 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.References
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[Bes] L.Bessieres. Sur le volume minimal des variétés ouvertes. Ann. Inst. Fourier (Grenoble) 50 (2000), pp.965-980.
[BCG] G.Besson, G.Courtois & S.Gallot. Entropies et rigidités des espaces localement symétriques. Geometric and Functional Analysis 5 (1995), pp.731-799.
[CF] C.Connell & B.Farb. Minimal entropy rigidity for lattices in products of rank one symmetric spaces. Preprint: math.uchicago.edu/ farb/papers.html.
[Gr] M.Gromov. Volume and bounded cohomology. Publ. Math IHES 56, (1981), pp.213-307.
[Ma] A.Manning. Topological entropy for geodesic flows. Ann. Math. 110 (1979), pp.565-573.
[Pa] G.Paternain. Geodesic flows. Birkhäuser (1999).
[1] G. Prasad. Strong rigidity of Q-rank 1 lattices. Inv. Math. 21 (1973), pp.255-286.
Published
2002-05-01
How to Cite
[1]
A. Navas, “On the volumetric entropy in the non compact case”, Proyecciones (Antofagasta, On line), vol. 21, no. 1, pp. 97-108, May 2002.
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Copyright (c) 2002 Proyecciones. Journal of Mathematics
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