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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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Monotonicity of maximal equicontinuous factors and an application to toral flows
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by T. Hauser and T. Jäger PDF
Proc. Amer. Math. Soc. 147 (2019), 4539-4554 Request permission

Abstract:

We show that for group actions on locally connected spaces the maximal equicontinuous factor map is always monotone, that is, the preimages of single points are connected. As an application, we obtain that if the maximal equicontinuous factor of a homeomorphism of the two-torus is minimal, then it is either (i) an irrational translation of the two-torus, (ii) an irrational rotation on the circle, or (iii) the identity on a singleton.
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Additional Information
  • T. Hauser
  • Affiliation: Faculty of Mathematics and Computer Science Institute of Mathematics, Friedrich Schiller University, 07737 Jena, Germany
  • Email: till.hauser@uni-jena.de
  • T. Jäger
  • Affiliation: Faculty of Mathematics and Computer Science Institute of Mathematics, Friedrich Schiller University, 07737 Jena, Germany
  • Email: tobias.jaeger@uni-jena.de
  • Received by editor(s): November 17, 2017
  • Received by editor(s) in revised form: December 21, 2018, and January 21, 2019
  • Published electronically: May 29, 2019
  • Additional Notes: The second author was supported by a Heisenberg professorship of the German Research Council (DFG grant OE 538/6-1). The project was also supported by the DFG project Dynamics on surfaces (DFG grant OE 538/9-1).
  • Communicated by: Wenxian Shen
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4539-4554
  • MSC (2010): Primary 54H20; Secondary 37B05, 37E30
  • DOI: https://doi.org/10.1090/proc/14562
  • MathSciNet review: 4002562