Statistical properties for nonhyperbolic maps with finite range structure |
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Authors: | Michiko Yuri |
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Affiliation: | Department of Business Administration, Sapporo University, Nishioka, Toyohira-ku, Sapporo 062, Japan |
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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 -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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