Related papers: Topological mixing for substitutions on two letter…
We investigate topological mixing of compatible random substitutions. For primitive random substitutions on two letters whose second eigenvalue is greater than one in modulus, we identify a simple, computable criterion which is equivalent…
We prove that a continuous linear operator $T$ on a topological vector space $X$ with weak topology is mixing if and only if the dual operator $T'$ has no finite dimensional invariant subspaces. This result implies the characterization of…
We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts…
The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…
The paper investigates H\"older and log-H\"older regularity of spectral measures for weakly mixing substitutions and the related question of quantitative weak mixing. It is assumed that the substitution is primitive, aperiodic, and its…
The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…
We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random…
We study the topology and dynamics of subshifts and tiling spaces associated to non-primitive substitutions in one dimension. We identify a property of a substitution, which we call tameness, in the presence of which most of the possible…
Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate…
We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) \theta : 0 \rightarrow 001,1 \rightarrow 11001 and (2) \eta : 0 \rightarrow 001,1 \rightarrow 11100. We show that the substitution…
We investigate the dynamics of tiling dynamical systems and their deformations. If two tiling systems have identical combinatorics, then the tiling spaces are homeomorphic, but their dynamical properties may differ. There is a natural map…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…
In this note we study the weak topology on paired modules over a (not necessarily commutative) ground ring. Over QF rings we are able to recover most of the well known properties of this topology in the case of commutative base fields. The…
A minimal system $(X,T)$ is topologically mildly mixing if all non-empty open subsets $U,V$, $\{n\in \Z: U\cap T^{-n}V\neq \emptyset\}$ is an IP$^*$-set. In this paper we show that if a minimal system is topologically mildly mixing, then it…
We show that a residual set of non-degenerate IETs on more than 3 letters is topologically mixing. This shows that there exists a uniquely ergodic topologically mixing IET. This is then applied to show that some billiard flows in a fixed…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling…
Topological mating is an combination that takes two same-degree polynomials and produces a new map with dynamics inherited from this initial pair. This process frequently yields a map that is Thurston-equivalent to a rational map $F$ on the…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…