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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.

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Ergodic universality of some topological dynamical systems
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by Anthony Quas and Terry Soo PDF
Trans. Amer. Math. Soc. 368 (2016), 4137-4170 Request permission


The Krieger generator theorem says that every invertible ergodic measure-preserving system with finite measure-theoretic entropy can be embedded into a full shift with strictly greater topological entropy. We extend Krieger’s theorem to include toral automorphisms and, more generally, any topological dynamical system on a compact metric space that satisfies almost weak specification, asymptotic entropy expansiveness, and the small boundary property. As a corollary, one obtains a complete solution to a natural generalization of an open problem in Halmos’s 1956 book regarding an isomorphism invariant that he proposed.
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Additional Information
  • Anthony Quas
  • Affiliation: Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, BC V8W 3R4, Canada
  • MR Author ID: 317685
  • Email:
  • Terry Soo
  • Affiliation: Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom
  • Address at time of publication: Department of Mathematics, University of Kansas, 405 Snow Hall, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045-7594
  • MR Author ID: 888642
  • Email:,
  • Received by editor(s): November 2, 2012
  • Received by editor(s) in revised form: April 9, 2014
  • Published electronically: July 10, 2015
  • Additional Notes: Both authors were funded in part by NSERC and MSRI
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 4137-4170
  • MSC (2010): Primary 37A35
  • DOI:
  • MathSciNet review: 3453367