Monatsh Math (2018) 185:415–441
Circularly ordered dynamical systems
· Michael Megrelishvili
Received: 13 September 2016 / Accepted: 1 November 2017 / Published online: 13 November 2017
© Springer-Verlag GmbH Austria, part of Springer Nature 2017
Abstract We study topological properties of circularly ordered dynamical systems
and prove that every such system is representable on a Rosenthal Banach space, hence,
is also tame. We derive some consequences for topological groups. We show that
several Sturmian like symbolic Z
-systems are circularly ordered. Using some old
results we characterize circularly ordered minimal cascades.
Keywords Circular order · Linear order · Enveloping semigroup · Tame dynamical
system · Sturmian system · Subshift · Symbolic system · Rosenthal space
Mathematics Subject Classiﬁcation Primary 37Bxx · 46-xx; Secondary 54H15 ·
Communicated by A. Constantin.
This research was supported by a grant of the Israel Science Foundation (ISF 668/13).
Department of Mathematics, Tel-Aviv University, Ramat Aviv, Israel
Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel