Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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.

 

On dynamical systems with the specification property
HTML articles powered by AMS MathViewer

by Karl Sigmund PDF
Trans. Amer. Math. Soc. 190 (1974), 285-299 Request permission

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
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
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 190 (1974), 285-299
  • MSC: Primary 28A65; Secondary 54H20
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0352411-X
  • MathSciNet review: 0352411