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 language | English |
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Pages (from-to) | 3941-3951 |
Number of pages | 11 |
Journal | Proceedings of the American Mathematical Society |
Volume | 136 |
Issue number | 11 |
DOIs | |
State | Published - Nov 2008 |