Flexibility of statistical properties for smooth systems satisfying the central limit theorem

Abstract

We exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: Zero entropy; Weak but not strong mixing; (Polynomial) mixing but not K; K but not Bernoulli and mixing at arbitrary fast polynomial rate. We also give an example of a system satisfying the CLT where the normalizing sequence is regularly varying with index 1. All these examples are C ∞ except for a zero entropy diffeomorphism satisfying the CLT which can be made C r for an arbitrary finite r. [ABSTRACT FROM AUTHOR]

Copyright of Inventiones Mathematicae is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)