WIAS Preprint No. 245, (1996)

Dimension of hyperbolic measures - A proof of the Eckmann-Ruelle conjecture


  • Barreira, Luis
  • Pesin, Yakov
  • Schmeling, Jörg
    ORCID: 0000-0001-6956-9463

2010 Mathematics Subject Classification

  • 58F11 28D05


  • Eckmann-Ruelle conjecture, hyperbolic measures, pointwise dimension




We prove the long-standing Eckmann-Ruelle conjecture in dimension theory of smooth dynamical systems. Namely, we show that the pointwise dimension exists almost everywhere with respect to a Borel probability measure with non-zero Lyapunov exponents invariant under a C1+α diffeomorphism of a smooth Riemannian manifold. This implies in particular that the Hausdorff dimension and box dimension of the measure as well as some other characteristics of dimension type of the measure coincide.

Appeared in

  • ERA-AMS 2 (1996), No. 1

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