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)


On dynamical systems with the specification property

Author: Karl Sigmund
Journal: Trans. Amer. Math. Soc. 190 (1974), 285-299
MSC: Primary 28A65; Secondary 54H20
MathSciNet review: 0352411
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A continuous transformation T of a compact metric space X satisfies the specification property if one can approximate distinct pieces of orbits by single periodic orbits with a certain uniformity. There are many examples of such transformations which have recently been studied in ergodic theory and statistical mechanics. This paper investigates the relation between Tinvariant measures and the frequencies of T-orbits. In particular, it is shown that every invariant measure (and even every closed connected subset of such measures) has generic points, but that the set of all generic points is of first category in X. This generalizes number theoretic results concerning decimal expansions and normal numbers.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28A65, 54H20

Retrieve articles in all journals with MSC: 28A65, 54H20

Additional Information

PII: S 0002-9947(1974)0352411-X
Keywords: Ergodic measures, generic points, quasiregular points, normal numbers
Article copyright: © Copyright 1974 American Mathematical Society

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