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Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities

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Abstract

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the central limit theorem and a vector-valued almost sure invariance principle. We also obtain results on decay of correlations and large deviations.

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Author notes

  1. Ian Melbourne

    Present address: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

Authors and Affiliations

  1. Mathematics Section, Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy

    Stefano Luzzatto

  2. Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK

    Ian Melbourne

Authors
  1. Stefano Luzzatto
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  2. Ian Melbourne
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Correspondence to Stefano Luzzatto.

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Communicated by G. Gallavotti

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Luzzatto, S., Melbourne, I. Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities. Commun. Math. Phys. 320, 21–35 (2013). https://doi.org/10.1007/s00220-013-1709-y

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  • DOI: https://doi.org/10.1007/s00220-013-1709-y

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