Almost Periodicity in Chaos

Almost Periodicity and Distributional Chaos in Banach Space

Let (X, ‖ · ‖) be a Banach space, f : X → X continous Freche’t differentiable map.Denote the set of almost periodic point by A(f).In this paper,we prove that there exists an uncountable set Λ such that f |Λ is distributionally chaotic,and Λ ⊂ A(f).

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...

Pointwise almost periodicity in a generalized shift dynamical system

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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...