Morphisms and almost-periodicity

Periodicity, morphisms, and matrices

In 1965, Fine and Wilf proved the following theorem: if (fn)n¿0 and (gn)n¿0 are periodic sequences of real numbers, of period lengths h and k, respectively, and fn = gn for 06 n¡h+ k − gcd(h; k), then fn = gn for all n¿ 0. Furthermore, the constant h + k − gcd(h; k) is best possible. In this paper, we consider some variations on this theorem. In particular, we study the case where fn 6 gn inste...

Periodicity and Almost-periodicity

Almost periodicity and discrete almost periodicity in semiflows

A theory of semiflows with a discrete acting topological semigroup was developed in the 2000 paper by D. Ellis, R. Ellis and M. Nerurkar ([2]). A theory for the case of an arbitrary acting topological semigroup has still to be developed. This paper can be considered as the beginning of an attempt in that direction. We discuss almost periodicity and G-almost periodicity of points in a semiflow a...

Quasicrystals and almost periodicity

We introduce a topology T on the space U of uniformly discrete subsets of the Euclidean space. Assume that S in U admits a unique autocorrelation measure. The diffraction measure of S is purely atomic if and only if S is almost periodic in (U,T ). This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to...

Cocycles and Almost Periodicity

We discuss different types of almost periodicity of trajectories of cocycles on compact solenoidal groups in relation to various notions of triviality of these cocycles. Introduction Let G be a compact solenoidal group, that is, a compact Abelian group containing, as a dense subgroup, the image of IR by a continuous homomorphism, say a. We shall assume that G is not a circle by requiring a to b...