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Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities |
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| Authors: | Stefano Luzzatto Ian Melbourne |
| Affiliation: | 1. Mathematics Section, Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy 2. Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK 3. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK |
| 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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