Inventiones mathematicae

, Volume 140, Issue 2, pp 351–398 | Cite as

SRB measures for partially hyperbolic systems whose central direction is mostly expanding

  • José F. Alves
  • Christian Bonatti
  • Marcelo Viana


We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms – the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting – under the assumption that the complementary subbundle is non-uniformly expanding. If the rate of expansion (Lyapunov exponents) is bounded away from zero, then there are only finitely many SRB measures. Our techniques extend to other situations, including certain maps with singularities or critical points, as well as diffeomorphisms having only a dominated splitting (and no uniformly hyperbolic subbundle).


Lyapunov Exponent Tangent Bundle Hyperbolic System Central Direction Invariant Subbundles 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • José F. Alves
    • 1
  • Christian Bonatti
    • 2
  • Marcelo Viana
    • 3
  1. 1.Dep. Matemática Pura, Faculdade de Ciências do Porto, P-4099-002 Porto, Portugal¶(e-mail:
  2. 2.Lab. Topologie, CNRS – UMR 5584, Univ. Bourgogne, B.P. 47870, 21078 Dijon Cedex, France (e-mail:
  3. 3.IMPA, Estrada D. Castorina 110, Jardim Botânico, 22460-320 Rio de Janeiro RJ, Brazil¶(e-mail:

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