Statistical properties of nonuniformly expanding 1d maps with logarithmic singularities

Details Statistical properties of nonuniformly expanding 1d maps with logarithmic singularities Statistical properties of nonuniformly expanding 1d maps with logarithmic singularities

2010-09-25

arxiv.org/abs/1009.5015v1

Nonlinearity 25 (2012) 551-567

Mathematics

Dynamical Systems

19 pages

Scientific paper

For a certain parametrized family of maps on the circle, with critical points and logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed in [19], corresponding to maps which exhibit nonuniformly hyperbolic behavior. For these parameters, we prove the existence of absolutely continuous invariant measures with good statistical properties, such as exponential decay of correlations. Combining our construction with the logarithmic nature of the singularities, we obtain a positive variance in Central Limit Theorem, for any nonconstant H\"older continuous observable.

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