2025/12/15 by Gabriel Fuhrmann, Chunlin Liu, Fuhrmann, Gabriel +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2512.13341
openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
We study minimal idempotents Jmin(X) in the Ellis semigroup E(X) associated with a Floyd-Auslander system (X,T). We show that (X,T) is non-tame if and only if |Jmin(X)| > 2ℵ0, which happens exactly when the factor map onto the maximal equicontinuous factor possesses uncountably many non-invertible fibres. This yields an easy-to-check criterion for distinguishing tame from non-tame Floyd-Auslander systems and, more importantly, provides an entire family of regular almost automorphic systems with |Jmin(X)| > 2ℵ0. Notably, all previously known regular almost automorphic non-tame systems exhibited only a small (i.e. ≤ 2ℵ0) set of minimal idempotents. We obtain our result by leveraging an alternative characterisation of (non)-tameness through, what we call, choice domains.