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Session 16. Ergodic Theory and Dynamical Systems
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On higher order regional proximality for arbitrary group actions |
Yonatan Gutman, Polish Academy of Sciences & University of Oxford, Poland/UK
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Ellis & Gottschalk introduced the regional proximal relation in
1960 whereas the higher order regional proximal relations for
Abelian group actions were introduced by Host, Kra \& Maass in
2010. The interest in these relations lies in their role in the
structural theory of topological dynamical systems. For example, for
amenable minimal group actions the regional proximal relation is an
equivalence relation. Moreover the quotient by this equivalence
relation is the maximal equicontinuous factor. In this talk I will
discuss a generalization of the higher order regional proximal
relations suitable for an arbitrary acting group. We will show that
for distal actions this relation is an equivalence relation and
explore its relation to structural theory. Joint work with Freddie
Manners and Péter Varjú.
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