Ellis enveloping semigroup for almost canonical model sets of an Euclidean space

Abstract

We consider certain point patterns of an Euclidean space and calculate the Ellis enveloping semigroup of their associated dynamical systems. The algebraic structure and the topology of the Ellis semigroup, as well as its action on the underlying space, are explicitly described. As an example, we treat the vertex pattern of the AmmanBeenker tiling of the plane. 37B50, 37B05

On tameness of almost automorphic dynamical systems for general groups

“…Thus, (T, G) is a factor of (X f , G). Further, note that (2.4) implies that π is almost one-to-one which hence proves (2). Finally, we prove that (1) implies (2).…”

“…Further, note that (2.4) implies that π is almost one-to-one which hence proves (2). Finally, we prove that (1) implies (2). To this end, suppose that we have an almost automorphic system (K, G) with the maximal equicontinuous factor (T, G) and let π : K → T be the associated factor map.…”

Circularly ordered dynamical systems

“…One may get in this way c-ordered subshifts X ⊂ {0, 1} Z which are not Sturmian (with complexity greater than p(n) = n + 1). (2) At least for the case of k = 1, the tameness of the corresponding symbolic Z-systems coming from coding functions of Definition 5.2 can be proved also by results of Pikula [39] and Aujogue [2]. Proof.…”

Combinatorial independence and naive entropy

“…The notion of tame actions was introduced by Köhler [36] motivated by Rosenthal's characterization of Banach spaces containing 1 [44] and is well studied [1, 9, 13-22, 24, 30, 32, 35, 38, 43]. Denote by C(X ) the space of all continuous R-valued functions on X equipped with the supremum norm.…”