Polyhedral Billiards, Eigenfunction Concentration and Almost Periodic Control

Tobias Wichtrey Control Systems with Almost Periodic

Characterization of almost maximally almost-periodic groups

Let G be an abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n(G, τ) of (G, τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n(n(G)) 6= n(G) if and only if n(G) is not dually embedded. In particular, n(n(Z, τ)) = n(Z, τ) for any Hausdorff group topology τ on Z. We shall write our a...

Equicontinuity and Almost Periodic Functions1

Let A be a separated uniform space, C(X, X) the set of continuous functions of X into X, and C(X) the set of real valued continuous functions on X provided with the topology of uniform convergence. For fEC(X) and aEC(X, X), fa will denote that element of C(X) such that (fa)(x) =f(xa)(xEX). Let fEC(X) and A EC(X, X). Then f is said to be almost periodic with respect to A if fA = [fa\ aEA ] is a ...

Almost Periodic Oscillations and Waves

Exponents and Almost Periodic Orbits

We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Čech cohomology group of the closure of the image of the map. We show that this group generalizes the subgroup of the reals generated by the Fourier-Bohr exponents of an almost periodic orbit and that any minimal almost periodic flow in a complete metric s...