Monotonicity of maximal equicontinuous factors and an application to toral flows

Hauser, T.; Jäger, T.

doi:10.1090/proc/14562

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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