Geodesic
On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture
Barreira, Luis1 ; Pesin, Yakov1 ; Schmeling, Jörg2
1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A.
2 Weierstrass Institute of Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany
Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 1, pp. 69-72.

Voir la notice de l'article provenant de la source American Mathematical Society

We prove the long-standing Eckmann–Ruelle conjecture in dimension theory of smooth dynamical systems. We show that the pointwise dimension exists almost everywhere with respect to a compactly supported Borel probability measure with non-zero Lyapunov exponents, invariant under a $C^{1+\alpha }$ diffeomorphism of a smooth Riemannian manifold.
DOI : 10.1090/S1079-6762-96-00007-8

Barreira, Luis 1 ; Pesin, Yakov 1 ; Schmeling, Jörg 2

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A.
2 Weierstrass Institute of Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany 
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Barreira, Luis; Pesin, Yakov; Schmeling, Jörg. On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture. Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 1, pp. 69-72. doi : 10.1090/S1079-6762-96-00007-8. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-96-00007-8/

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[6] Young, Lai Sang Dimension, entropy and Lyapunov exponents Ergodic Theory Dynam. Systems 1982 109 124

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