Israel Journal of Mathematics

, Volume 219, Issue 1, pp 171–188 | Cite as

Disintegration of invariant measures for hyperbolic skew products



We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from an observable v on the skew product to an observable \(\overline v \) on the system quotiented along stable manifolds. Under mild assumptions on the system we prove that the disintegration preserves the smoothness of v, first in the case where v is Hölder and second in the case where v is \({\mathcal{C}^1}\) .


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  1. [1]
    V. Araújo, O. Butterley and P. Varandas, Open sets of Axiom A flows with exponentially mixing attractors, Proceedings of the American Mathematical Society 144 (2016), 2971–2984.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    V. Araújo, I. Melbourne and P. Varandas, Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps, Communications in Mathematical Physics 340 (2015), 901–938.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    V. Araújo, M. J. Pacifico, E. R. Pujals and M. Viana, Singular-hyperbolic attractors are chaotic, Transactions of the American Mathematical Society 361 (2009), 2431–2485.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    V. Araújo and P. Varandas, Robust exponential decay of correlations for singular-flows, Communications in Mathematical Physics 311 (2012), 215–246.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    A. Avila, S. Gouëzel and J.-C. Yoccoz, Exponential mixing for the Teichmüller flow, Publications Mathématiques. Institut de Hautes Études Scientifiques 104 (2006), 143–211.CrossRefMATHGoogle Scholar
  6. [6]
    R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lect. Notes in Mathematics, Vol. 470, Springer Verlag, Berlin–New York, 1975.Google Scholar
  7. [7]
    S. Galatolo and M. J. Pacifico, Lorenz like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence, Ergodic Theory and Dynamical Systems 30 (2010), 1703–1737.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    V. A. Rohlin, On the fundamental ideas of measure theory, American Mathematical Society Translations 71 (1952).Google Scholar

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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität WienWienAustria
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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