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

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

Published electronically:
February 14, 2000

MathSciNet review:
1695039

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Received by editor(s):
February 20, 1998

Published electronically:
February 14, 2000

Article copyright:
© Copyright 2000
American Mathematical Society