We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian
perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall …

We prove that all the solutions of a quasi-periodically forced linear Klein-Gordon equation
$\psi_ {tt}-\psi_ {xx}+\mathtt {m}\psi+ Q (\omega t)\psi= 0$ where $ Q (\omega t) …

In this article, we prove a reducibility result for the linear Schrödinger equation on a Zoll
manifold with quasi-periodic in time pseudo-differential perturbation of order less than or …

We consider the one-dimensional quantum harmonic oscillator perturbed by a linear
operator which is a polynomial of degree 2 in (x,-i∂ x), with coefficients quasi-periodically …

We prove the reducibility of quantum harmonic oscillators in R d perturbed by a quasi-
periodic in time potential V (x, ω t) with logarithmic decay. By a new estimate built for solving …

We prove the reducibility of 1-D quantum harmonic oscillators in $\mathbb R $ perturbed by
a quasi-periodic in time potential $ V (x,\omega t) $ under the following conditions, namely …

For a family of 1-d quantum harmonic oscillators with a perturbation which is C 2
parametrized by E∈ I⊂ R and quadratic on x and− i∂ x with coefficients quasi-periodically …

In the present paper, we prove an infinite dimensional reversible Kolmogorov-Arnold-Moser
(KAM) theorem. As an application, we study the existence of KAM tori for a class of two …

In this paper, we prove that the Sobolev norms of solutions for the linear wave equation with
unbounded perturbations of order one remain bounded for all time. The main proof is based …

In this paper, we establish the reducibility of a class of linear coupled quantum harmonic
oscillator systems under time quasi-periodic, non-Hamiltonian, reversible perturbations. This …