On structure theorems and non-saturated examples

Abstract

For any minimal system (X, T ) and d ≥ 1 there is an associated minimal systemIn this paper, we further study the structure of N d (X). We show that the maximal distal factor of N d (X) is N d (X dis ) with X dis being the maximal distal factor of X, and prove that as minimal systems (N d (X), G d (T )) has the same structure theorem as (X, T ). In addition, a non-saturated metric example (X, T ) is constructed, which is not T × T 2 -saturated and is a Toeplitz minimal system.

Topological dynamical systems induced by polynomials and combinatorial consequences

“…We remark that the almost one to one modifications in the above theorem are needed, see for example [18,38]. Based on Theorem 3.1, using PET induction and elaborate constructions, it was shown in [34] Theorem 3.2.…”