Pure point spectrum for dynamical systems and mean, Besicovitch and Weyl almost periodicity

Pointwise almost periodicity in a generalized shift dynamical system

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Stability and Almost Periodicity in Dynamical Systems1

let x=(xi, • • ■ , xn) and /=(fi, • • • ,/„), and suppose that / is of class C1. A set, 12, of points x will be called unrestricted if, whenever a point x0 is in 12, the solution path x = x(t), where x0 = x(0), exists for — co </< oo and lies in 12. Two types of stability distinguished simply by "A" and "B" will be considered: (A) Let the value to be arbitrary but fixed. A solution x — x(t) of ...

Periodicity and Almost-periodicity

Pure Point Spectrum for Measure Dynamical Systems on Locally Compact Abelian Groups

We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems built from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our approach is based on a study of almost periodicity in a Hilbert space. It allows us to set up a perturbation theory for arbitrary equivariant measurable pertur...

On P Systems and Almost Periodicity

The study of P systems as a mathematical model for biological systems is an important research topic in the area of membrane computing. In this respect, the detection of periodicity and almost periodicity as aspects of the system dynamics seems to be of particular relevance for understanding many biological processes and their related phenomena. This paper introduces specific notions of periodi...