Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



Entropy dimension of topological dynamical systems

Authors: Dou Dou, Wen Huang and Kyewon Koh Park
Journal: Trans. Amer. Math. Soc. 363 (2011), 659-680
MSC (2000): Primary 37B99, 54H20
Published electronically: September 2, 2010
MathSciNet review: 2728582
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the notion of topological entropy dimension to measure the complexity of entropy zero systems. It measures the superpolynomial, but subexponential, growth rate of orbits. We also introduce the dimension set, $ \mathcal{D}(X,T)\subset [0,1]$, of a topological dynamical system to study the complexity of its factors. We construct a minimal example whose dimension set consists of one number. This implies the property that every nontrivial open cover has the same entropy dimension. This notion for zero entropy systems corresponds to the $ K$-mixing property in measurable dynamics and to the uniformly positive entropy in topological dynamics for positive entropy systems. Using the entropy dimension, we are able to discuss the disjointness between the entropy zero systems. Properties of entropy generating sequences and their dimensions have been investigated.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 37B99, 54H20

Retrieve articles in all journals with MSC (2000): 37B99, 54H20

Additional Information

Dou Dou
Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, People’s Republic of China – and – Department of Mathematics, Ajou University, Suwon 442-729, South Korea

Wen Huang
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

Kyewon Koh Park
Affiliation: Department of Mathematics, Ajou University, Suwon 442-729, South Korea

Keywords: Entropy dimension, dimension set, u.d. system
Received by editor(s): March 3, 2008
Received by editor(s) in revised form: August 29, 2008
Published electronically: September 2, 2010
Additional Notes: The second author was supported by NNSF of China, 973 Project and FANEDD (Grant No 200520).
The third author was supported in part by KRF-2007-313-C00044.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia