TODORČEVIĆ’ TRICHOTOMY AND A HIERARCHY IN THE CLASS OF TAME DYNAMICAL SYSTEMS

Eli Glasner; Michael Megrelishvili

doi:https://doi.org/10.1090/tran/8522

TODORČEVIĆ’ TRICHOTOMY AND A HIERARCHY IN THE CLASS OF TAME DYNAMICAL SYSTEMS

Eli Glasner, Michael Megrelishvili

Tel Aviv University, Bar-Ilan University

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

Abstract

Todorčević’ trichotomy in the class of separable Rosenthal compacta induces a hierarchy in the class of tame (compact, metrizable) dynamical systems (X,T) according to the topological properties of their enveloping semigroups E(X). More precisely, we define the classes Tame2 ⊂ Tame1 ⊂ Tame, where Tame1 is the proper subclass of tame systems with first countable E(X), and Tame2 is its proper subclass consisting of systems with hereditarily separable E(X). We study some general properties of these classes and exhibit many examples to illustrate these properties.

Original language	English
Pages (from-to)	4513-4548
Number of pages	36
Journal	Transactions of the American Mathematical Society
Volume	375
Issue number	7
DOIs	https://doi.org/10.1090/tran/8522
State	Published - 1 Jul 2022

Keywords

Almost automorphic system
Rosenthal compact
Sturmian system
circular order
enveloping semigroup
linear order
tame dynamical system

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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https://doi.org/10.1090/tran/8522

Cite this

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title = "TODOR{\v C}EVI{\'C}{\textquoteright} TRICHOTOMY AND A HIERARCHY IN THE CLASS OF TAME DYNAMICAL SYSTEMS",

abstract = "Todor{\v c}evi{\'c}{\textquoteright} trichotomy in the class of separable Rosenthal compacta induces a hierarchy in the class of tame (compact, metrizable) dynamical systems (X,T) according to the topological properties of their enveloping semigroups E(X). More precisely, we define the classes Tame2 ⊂ Tame1 ⊂ Tame, where Tame1 is the proper subclass of tame systems with first countable E(X), and Tame2 is its proper subclass consisting of systems with hereditarily separable E(X). We study some general properties of these classes and exhibit many examples to illustrate these properties.",

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author = "Eli Glasner and Michael Megrelishvili",

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AB - Todorčević’ trichotomy in the class of separable Rosenthal compacta induces a hierarchy in the class of tame (compact, metrizable) dynamical systems (X,T) according to the topological properties of their enveloping semigroups E(X). More precisely, we define the classes Tame2 ⊂ Tame1 ⊂ Tame, where Tame1 is the proper subclass of tame systems with first countable E(X), and Tame2 is its proper subclass consisting of systems with hereditarily separable E(X). We study some general properties of these classes and exhibit many examples to illustrate these properties.

KW - Almost automorphic system

KW - Rosenthal compact

KW - Sturmian system

KW - circular order

KW - enveloping semigroup

KW - linear order

KW - tame dynamical system

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M3 - مقالة

SN - 0002-9947

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -

TODORČEVIĆ’ TRICHOTOMY AND A HIERARCHY IN THE CLASS OF TAME DYNAMICAL SYSTEMS

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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