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 | |
| State | Published - 1 Jul 2022 |
Bibliographical note
Publisher Copyright:© 2022 American Mathematical Society
Funding
Received by the editors July 7, 2021. 2020 Mathematics Subject Classification. Primary 37Bxx; Secondary 54H15, 54H05, 54F05. Key words and phrases. Almost automorphic system, circular order, enveloping semigroup, linear order, Rosenthal compact, Sturmian system, tame dynamical system. This research was supported by a grant of the Israel Science Foundation (ISF 1194/19).
| Funders | Funder number |
|---|---|
| Israel Science Foundation | ISF 1194/19 |
Keywords
- Almost automorphic system
- Rosenthal compact
- Sturmian system
- circular order
- enveloping semigroup
- linear order
- tame dynamical system