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ISSN 1079-6762

 

On the pointwise dimension
of hyperbolic measures:
a proof of the Eckmann-Ruelle conjecture


Authors: Luis Barreira, Yakov Pesin and Jörg Schmeling
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 69-72
MSC (1991): Primary 58F11, 28D05
MathSciNet review: 1405971
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Abstract: 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.


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Additional Information

Luis Barreira
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A.
Email: luis@math.psu.edu

Yakov Pesin
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A.
Email: pesin@math.psu.edu

Jörg Schmeling
Affiliation: Weierstrass Institute of Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany
Email: schmeling@wias-berlin.de

DOI: http://dx.doi.org/10.1090/S1079-6762-96-00007-8
PII: S 1079-6762(96)00007-8
Keywords: Eckmann--Ruelle conjecture, hyperbolic measure, pointwise dimension
Received by editor(s): May 13, 1996
Additional Notes: This paper was written while L. B. was on leave from Instituto Superior Técnico, Department of Mathematics, at Lisbon, Portugal, and J. S. was visiting Penn State. L. B. was supported by Program PRAXIS XXI, Fellowship BD 5236/95, JNICT, Portugal. J. S. was supported by the Leopoldina-Forderpreis. The work of Ya. P. was partially supported by the National Science Foundation grant #DMS9403723.
Communicated by: Svetlana Katok
Article copyright: © Copyright 1996 American Mathematical Society