Recurrence times and rates of mixing

[BY] M. Benedicks and L.-S. Young,Decay or correlations for certain Henon maps, to appear in Astérisque, in a volume in honor of Douady.

[FL] A. Fisher and A. Lopes,Polynomial decay of correlation and the central limit theorem for the equilibrium state of a non-Hölder potential, preprint, 1997.

[HK] F. Hofbauer and G. Keller,Ergodic properties of invariant measures for piecewise monotonic transformations, Mathematische Zeitschrift180 (1982), 119–140.

[H] H. Hu,Decay of correlations for piecewise smooth maps with indifferent fixed points, preprint.

[HY] H. Hu and L.-S. Young,Nonexistence of SBRmeasures for some systems that are “almost Anosov”, Ergodic Theory and Dynamical Systems15 (1995), 67–76.

[I] S. Isola,On the rate of convergence to equilibrium for countable ergodic Markov chains, preprint, 1997.

[KV] C. Kipnis and S.R.S. Varadhan,Central limit theorem for additive functions of reversible Markov process and applications to simple exclusions, Communications in Mathematical Physics104 (1986), 1–19.

[L1] C. Liverani,Decay of correlations, Annals of Mathematics142 (1995), 239–301.

[L2] C. Liverani,Central limit theorem for deterministic systems, International Conference on Dynamical Systems, Montevideo 1995 (F. Ledrappier, J. Lewowicz and S. Newhouse, eds.), Pitman Research Notes in Mathematics362 (1996), 56–75.

[LSV] C. Liverani, B. Saussol and S. Vaienti,A probabilistic approach to intermittency, preprint.

[M] R. Mañé,Ergodic Theory and Differentiable Dynamics, Springer-Verlag, Berlin, 1983.

[Pi] G. Pianigiani,First return maps and invariant measures, Israel Journal of Mathematics35 (1980), 32–48.

[Po] M. Pollicott,Rates of mixing for potentials of summable variation, to appear in Transactions of the American Mathematical Society.

[Pt] J.W. Pitman,Uniform rates of convergence for Markov chain transition probabilities, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete29 (1974), 193–227.

[R] D. Ruelle,Thermodynamic Formalism, Addison-Wesley, New York, 1978.

[TT] P. Tuominen and R. Tweedie,Subgeometric rates of convergence of f-ergodic Markov chains, Advances in Applied Probability26 (1994), 775–798.

[Y] L.-S. Young,Statistical properties of dynamical systems with some hyperbolicity, Annals of Mathematics147 (1998), 558–650.