Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The first return time properties of an irrational rotation
HTML articles powered by AMS MathViewer

by Dong Han Kim and Kyewon Koh Park PDF
Proc. Amer. Math. Soc. 136 (2008), 3941-3951 Request permission

Abstract:

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.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37E10, 11K50
  • Retrieve articles in all journals with MSC (2000): 37E10, 11K50
Additional Information
  • Dong Han Kim
  • Affiliation: Department of Mathematics, The University of Suwon, Hwaseong 445-743, Korea
  • MR Author ID: 630927
  • Email: kimdh@suwon.ac.kr
  • Kyewon Koh Park
  • Affiliation: Department of Mathematics, Ajou University, Suwon 443-749, Korea
  • MR Author ID: 136240
  • Email: kkpark@ajou.ac.kr
  • Received by editor(s): June 1, 2007
  • Received by editor(s) in revised form: October 2, 2007
  • Published electronically: June 2, 2008
  • Additional Notes: The first author was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2007-331-C00016).
    The second author was supported in part by KRF 2007-313-C00044
  • Communicated by: Jane M. Hawkins
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3941-3951
  • MSC (2000): Primary 37E10, 11K50
  • DOI: https://doi.org/10.1090/S0002-9939-08-09388-X
  • MathSciNet review: 2425734