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

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

2011-08-30

arxiv.org/abs/1108.5948v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

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.

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