We study the ordinary differential equation εẍ+ ẋ+ εg(x) = εf(ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c0 ∈ R is such that g(c0) equals the average of f and g(c0) 6= 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c0 with frequency vector ω. We show that such a solution depends analytically on ε in...

The standard quantum discrete nonlinear Schrodinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. I f f -+ x at a sufficiently small level of anharmonicity c j ) , the value for soliton binding energy from quantum field‘theory (QFT) in the continuum limit is recovered. For fixed however, the QFT resul...

Recently, we investigated the effect of delay on the asymptotic behavior of the model ẋ+x = f (x(·−τ)) of population growth, when the nonlinearity f is a unimodal function. Now we prove that for large delay, there are several nonconstant (positive) periodic solutions. We also use knots theory to study periodic solutions with period 3τ . Some of our results do not rely on the continuity of f and...

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. Moreover, the 2-regular case is precisely the class of totally real number fields that have homotopy cartesian “Bökstedt square”, relating the K-theory of the 2-integers to that of the fields of real and co...

In this paper we consider the existence and uniqueness of bounded solutions of periodic evolution equations of the form u = A(t)u + ǫH(t, u) + f(t), where A(t) is an in general unbounded operator depending 1-periodically on t, H is periodic in t with the same period as A, ǫ is small, and f is a bounded and continuous function that is not necessarily uniformly continuous. We propose a new approa...

The behaviour of a driven double well Duffing-van der Pol (DVP) oscillator for a specific parametric choice (| α |= β) is studied. The existence of different attractors in the system parameters (f − ω) domain is examined and a detailed account of various steady states for fixed damping is presented. Transition from quasiperiodic to periodic motion through chaotic oscillations is reported. The i...

Analogs of almost periodic functions for the unit circle are introduced. Certain uniform algebras generated by such functions are studied, the corona theorems for them are proved, and their maximal ideal spaces are described. §1. Formulation of main results 1.1. The classical almost periodic functions on the real line, as first introduced by H. Bohr in the 1920s, play an important role in vario...

For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular...

For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular...

It was observed in [Su5] that the spectrum of a periodic Schrodinger operator on a Riemannian manifold has band structure if the transformation group acting on the manifold satisfies the Kadison property (see below for the definition). Here band structure means that the spectrum is a union of mutually disjoint, possibly degenerate closed intervals, such that any compact subset of R meets only f...