The first return time properties of an irrational rotation

Dong Han Kim, Kyewon Koh Park

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

If an ergodic system has positive entropy, then the Shannon- McMillan-Breiman theorem provides a relationship between the entropy and thesizeofan atom ofthe 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.

Original languageEnglish
Pages (from-to)3941-3951
Number of pages11
JournalProceedings of the American Mathematical Society
Volume136
Issue number11
DOIs
StatePublished - Nov 2008

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