Exponential Mixing: Lectures from Mumbai

  • Mark PollicottEmail author
Part of the Infosys Science Foundation Series book series (ISFS)


We discuss a number of results related to mixing and, in particular, to the rate of mixing. This is sometimes alternatively known as the rate of decay of correlations.


  1. 1.
    A. Avila, S. Gouzel and J.-C. Yoccoz, Exponential mixing for the Teichmller flow. Publ. Math. Inst. Hautes tudes Sci. No. 104 (2006), 143–211.CrossRefGoogle Scholar
  2. 2.
    V. Baladi and B. Vallée, Exponential decay of correlations for surface semi-flows without finite Markov partitions. Proc. Amer. Math. Soc. 133 (2005), no. 3, 865–874.MathSciNetCrossRefGoogle Scholar
  3. 3.
    V. Baladi and B. Vallée, Euclidean algorithms are Gaussian. J. Number Theory 110 (2005), no. 2, 331–386MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. Bowen, Invariant measures for Markov maps of the interval (With an afterword by Roy L. Adler and additional comments by Caroline Series) Comm. Math. Phys. 69 (1979), no. 1, 1–17MathSciNetCrossRefGoogle Scholar
  5. 5.
    P. Collet and J.-P. Eckmann, Iterated maps on the interval as dynamical systems. Progress in Physics, 1. Birkhuser, Boston, Mass., 1980.Google Scholar
  6. 6.
    W. Doeblin and R. Fortet, Sur des chanes à liaisons complètes, Bull. Soc. Math. France 65 (1937), 132–148.MathSciNetCrossRefGoogle Scholar
  7. 7.
    D. Dolgopyat, On decay of correlations in Anosov flows. Ann. of Math. (2) 147 (1998), no. 2, 357–390.MathSciNetCrossRefGoogle Scholar
  8. 8.
    D. Dolgopyat, On mixing properties of compact group extensions of hyperbolic systems, Israel J. Math. 130 (2002) 157–205.MathSciNetCrossRefGoogle Scholar
  9. 9.
    D. Hensley, Continued fractions, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006.CrossRefGoogle Scholar
  10. 10.
    H. Huber, Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen, Math. Ann. 138 1959 1–26.MathSciNetCrossRefGoogle Scholar
  11. 11.
    C.T. Ionescu Tulcea and G. Marinescu, Théorie ergodique pour des classes d’opérations non complètement continues, Ann. of Math. (2) 52, (1950). 140–147.Google Scholar
  12. 12.
    Donald E. Knuth, The art of computer programming, Vol. 2. Seminumerical algorithms, Addison-Wesley, Reading, MA, 2011.Google Scholar
  13. 13.
    A. Lasota and J. Yorke, On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc. 186 (1973) 481–488MathSciNetCrossRefGoogle Scholar
  14. 14.
    F. Ledrappier and S. Lim, Local Limit Theorem in negative curvature, Preprint.Google Scholar
  15. 15.
    J. Lee and H.-S. Sun, Another note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Valle, Acta Arith. 188 (2019), 241–251.Google Scholar
  16. 16.
    C. Liverani, On contact Anosov flows. Ann. of Math. (2) 159 (2004), no. 3, 1275–1312.MathSciNetCrossRefGoogle Scholar
  17. 17.
    F. Naud, Dolgopyat’s estimates for the modular surface, lecture notes from IHP June 2005, workshop “time at work”.Google Scholar
  18. 18.
    W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astrisque, 187–188, (1990) 268MathSciNetzbMATHGoogle Scholar
  19. 19.
    M. Pollicott and R. Sharp, Exponential error terms for growth functions on negatively curved surfaces. Amer. J. Math. 120 (1998) 1019–1042MathSciNetCrossRefGoogle Scholar
  20. 20.
    M. Reed and B. Simon, Methods of modern mathematical physics. I, Functional analysis. Academic Press, Inc., New York, 1980.Google Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WarwickCoventryUK

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