We prove that every eigenvalue of a Schrbdinger operator with an almost periodic potential acting in the space of all square Haar-integrable functions on the Bohr compactification of ~ has multiplicity not greater than 2.

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...

In this work, we study the existence of almost periodic solutions for some partial neutral functional differential equations. Using the variation of constants formula and the spectral decomposition of the phase space developed in [6], we prove that the existence of an almost periodic solution is equivalent to the existence of a bounded solution on R+.

Skew-product flow which is generated by a nonautonomous recurrent tridiagonal competitive-cooperative system of differential equations is considered. It is shown that any minimal set is an almost 1-1 extension of the base flow and any ω-limit set contains at most two minimal sets, which generalizes the results of J. Smillie [SIAM J. Math. Anal., 15(1984), pp. 530–534] in autonomous cases and H....

The Thue-Morse sequence is a classical example of an almost periodic (or uniformly recurrent) sequence in the sense that its associated symbolic dynamical system is minimal. We prove that the subsequence along squares of the Thue-Morse sequence is normal.

*Correspondence: [email protected] 1School of Mathematical Science, University of Science and Technology of China, Hefei, 230036, China 2School of Mathematics and Statistics, Hefei Normal University, Hefei, 230601, China Full list of author information is available at the end of the article Abstract This paper is concerned with a class of neutral Nicholson blowflies models with leakage delays...

It is shown in this paper that if BG is the Stone-ech compactification of a group G, and G satisfying a certain condition, then there is a weakly recurrent point in BG which is not almost periodic, and if another condition will be added, then there is a recurrent point in 8G which is not almost periodic point.

In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type II1 with prescribed fundamental group. First we investigate state-preserving group actions on the almost periodic free Araki-Woods factors satisfying both a condition of mixing and a condition of free malleability in the sense of Popa. Typical examples are given by the fr...

We consider abstract differential equations of the form u′(t) = Au(t)+f(t) or u′′(t)=Au(t)+f(t) in Banach spaces X, where f(·), R→X is almost-periodic, while A is a linear operator, (A)⊂X →X. If the solution u(·) is likewise almost-periodic, R→X, we establish connections between their Bohr-transforms, û(λ) and f̂ (λ). 2000 Mathematics Subject Classification. 34C27, 34G10.

This paper considers the existence of positive almost-periodic solutions for almost-periodic LotkaVolterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.