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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reflections on equicontinuity


Authors: Joseph Auslander, Gernot Greschonig and Anima Nagar
Journal: Proc. Amer. Math. Soc. 142 (2014), 3129-3137
MSC (2010): Primary 37B05, 54H20
Published electronically: May 19, 2014
MathSciNet review: 3223369
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Abstract: We study different conditions which turn out to be equivalent to equicontinuity for a transitive compact Hausdorff flow with a general group action. Among them are a notion of ``regional'' equicontinuity, also known as the ``Furstenberg'' condition, and the condition that every point of the phase space is almost automorphic. Then we study relations on the phase space arising from dynamical properties, among them the regionally proximal relation and two relations introduced by Veech. We generalize Veech's results for minimal actions of non-Abelian groups preserving a probability measure with respect to the regionally proximal relation. We provide proofs in the framework of dynamical systems rather than harmonic analysis as given by Veech.


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Additional Information

Joseph Auslander
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: jna@math.umd.edu

Gernot Greschonig
Affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
Email: greschg@fastmail.net

Anima Nagar
Affiliation: Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India
Email: anima@maths.iitd.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12034-X
PII: S 0002-9939(2014)12034-X
Keywords: Compact flows, equicontinuity, almost automorphic points
Received by editor(s): May 2, 2012
Received by editor(s) in revised form: September 21, 2012
Published electronically: May 19, 2014
Additional Notes: The second author was supported by the research project S9614 of the Austrian Science Fund (FWF)
Communicated by: Yingfei Yi
Article copyright: © Copyright 2014 American Mathematical Society