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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Statistical properties for nonhyperbolic maps with finite range structure


Author: Michiko Yuri
Journal: Trans. Amer. Math. Soc. 352 (2000), 2369-2388
MSC (2000): Primary 11K50, 11K55, 28D05, 58F03, 58F11, 58F15
Published electronically: February 14, 2000
MathSciNet review: 1695039
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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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Additional Information

Michiko Yuri
Affiliation: Department of Business Administration, Sapporo University, Nishioka, Toyohira-ku, Sapporo 062, Japan
Email: yuri@math.sci.hokudai.ac.jp, yuri@math-ext.sapporo-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02579-4
PII: S 0002-9947(00)02579-4
Received by editor(s): February 20, 1998
Published electronically: February 14, 2000
Article copyright: © Copyright 2000 American Mathematical Society