论文信息 - ARE IRRATIONAL

ARE IRRATIONAL

. If an ergodic system has positive entropy, then the Shannon-McMillan-Breiman theorem provides a relationship between the entropy and the size of an atom of the iterated partition. The system also has Ornstein-Weiss’ ﬁrst return time property, which oﬀers a method of computing the entropy via an orbit. We consider irrational rotations which are the simplest model of zero entropy. We prove that almost every irrational rotation has the analogous properties if properly normalized. However there are some irrational rotations that exhibit diﬀerent behavior.

Tim Jones | N O N Z E R O Z E R O S O F T H E H E R M I T E P O

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