2020/11/09 by Eli Glasner, Michael Megrelishvili, Glasner, Eli +1 · 3 citations
Mathematics · #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2011.04376
Todorcević' 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.