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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.

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Dynamical simplices and minimal homeomorphisms
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by Tomás Ibarlucía and Julien Melleray PDF
Proc. Amer. Math. Soc. 145 (2017), 4981-4994 Request permission

Abstract:

We give a characterization of sets $K$ of probability measures on a Cantor space $X$ with the property that there exists a minimal homeomorphism $g$ of $X$ such that the set of $g$-invariant probability measures on $X$ coincides with $K$. This extends theorems of Akin (corresponding to the case when $K$ is a singleton) and Dahl (when $K$ is finite-dimensional). Our argument is elementary and different from both Akin’s and Dahl’s.
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Additional Information
  • Tomás Ibarlucía
  • Affiliation: Université de Lyon, Université Claude Bernard – Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
  • MR Author ID: 1161335
  • Julien Melleray
  • Affiliation: Université de Lyon, Université Claude Bernard – Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
  • Address at time of publication: Institut de Math’ematiques de Jussieu–PRG, Université Paris 7, case 7012, 75205 Parist cedex 13, France
  • MR Author ID: 781936
  • Received by editor(s): December 11, 2015
  • Received by editor(s) in revised form: October 28, 2016
  • Published electronically: April 4, 2017
  • Additional Notes: Research partially supported by Agence Nationale de la Recherche projects GruPoLoCo (ANR-11-JS01-0008) and ValCoMo (ANR-13-BS01-0006).
  • Communicated by: Nimish Shah
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4981-4994
  • MSC (2010): Primary 54H20; Secondary 37B05
  • DOI: https://doi.org/10.1090/proc/13578
  • MathSciNet review: 3692011