Statistical properties for nonhyperbolic maps with finite range structure

Yuri, Michiko

doi:10.1090/S0002-9947-00-02579-4

Statistical properties for nonhyperbolic maps with finite range structure
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by Michiko Yuri

Trans. Amer. Math. Soc. 352 (2000), 2369-2388

DOI: https://doi.org/10.1090/S0002-9947-00-02579-4

Published electronically: February 14, 2000

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Abstract:

We establish the central limit theorem and non-central limit theorems for maps admitting indifferent periodic points (the so-called intermittent maps). We also give a large class of Darling-Kac sets for intermittent maps admitting infinite invariant measures. The essential issue for the central limit theorem is to clarify the speed of $L^1$-convergence of iterated Perron-Frobenius operators for multi-dimensional maps which satisfy Renyi’s condition but fail to satisfy the uniformly expanding property. Multi-dimensional intermittent maps typically admit such derived systems. There are examples in section 4 to which previous results on the central limit theorem are not applicable, but our extended central limit theorem does apply.

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