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Proceedings of the American Mathematical Society

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Monotonicity of maximal equicontinuous factors and an application to toral flows


Authors: T. Hauser and T. Jäger
Journal: Proc. Amer. Math. Soc. 147 (2019), 4539-4554
MSC (2010): Primary 54H20; Secondary 37B05, 37E30
DOI: https://doi.org/10.1090/proc/14562
Published electronically: May 29, 2019
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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

DOI: https://doi.org/10.1090/proc/14562
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
Article copyright: © Copyright 2019 American Mathematical Society