Circularly ordered dynamical systems

Eli Glasner; Michael Megrelishvili

doi:10.1007/s00605-017-1134-y

Circularly ordered dynamical systems

Eli Glasner^*, Michael Megrelishvili

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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^k-systems are circularly ordered. Using some old results we characterize circularly ordered minimal cascades.

Original language	English
Pages (from-to)	415-441
Number of pages	27
Journal	Monatshefte fur Mathematik
Volume	185
Issue number	3
DOIs	https://doi.org/10.1007/s00605-017-1134-y
State	Published - 1 Mar 2018

Keywords

Circular order
Enveloping semigroup
Linear order
Rosenthal space
Sturmian system
Subshift
Symbolic system
Tame dynamical system

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10.1007/s00605-017-1134-y

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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 Zk-systems are circularly ordered. Using some old results we characterize circularly ordered minimal cascades.",

keywords = "Circular order, Enveloping semigroup, Linear order, Rosenthal space, Sturmian system, Subshift, Symbolic system, Tame dynamical system",

author = "Eli Glasner and Michael Megrelishvili",

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KW - Linear order

KW - Rosenthal space

KW - Sturmian system

KW - Subshift

KW - Symbolic system

KW - Tame dynamical system

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Circularly ordered dynamical systems

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Keywords

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