There are several notions of the ‘dual’ of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of… (More)

Let (>“, (+l)n) be the adic system associated to the substitution: 1 + 12,. , (n 1) + In, n + 1. In Sirvent (1996) it was shown that there exist a subset ‘%” of _P and a map h, : W’ + V” such that… (More)

where β = β(β−1)−1, M ∈ N∪{∞}, and l0, l1, . . . is a uniquely determined (finite or infinite) sequence of non-negative integers (cf. [2]). Analogously to other types of expansions we may ask for… (More)

Article history: Received 21 October 2013 Received in revised form 3 December 2013 Accepted 12 December 2013 Available online 14 January 2014 Communicated by Arne Winterhof MSC: 11B84 11K16 12E20… (More)

In this article we study the common dynamics of two different Pisot substitutions σ1 and σ2 having the same incidence matrix. This common dynamics arises in the study of the adic systems associated… (More)

Let (X, f) be a topological dynamical system. We say that it is partially periodic point free up to period n, if f does not have periodic points of periods smaller than n + 1. When X is a compact… (More)

In this article, we introduce a family of weighted lattice paths, whose step set is {H = (1, 0), V = (0, 1), D1 = (1, 1), . . . , Dm−1 = (1,m − 1)}. Using these lattice paths, we define a family of… (More)

In this paper we shall associate a semigroup with the &-bonacci numbers, which describes the self-similar structure of the dynamical system associated with the substitution 1 -> 12, ...(& -1) -» Ik,… (More)