In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

Floquet theory provides rigorous foundations for the theory of periodically driven quantum
systems. In the case of non-periodic driving, however, the situation is not so well understood …

We show how a large family of interacting nonequilibrium phases of matter can arise from
the presence of multiple time-translation symmetries, which occur by quasiperiodically …

The total number of such permutations is equal to (n—1)(«—2)/2. Some of them are rotations
(isomorphic to the addition of a constant to the residues modn). But it is not clear what …

Despite its long history, a canonical formulation of quantum ergodicity that applies to general
classes of quantum dynamics, including driven systems, has not been fully established …

In this paper, we prove that a quasi-periodic linear differential equation in sl (2, ℝ) with two
frequencies (α, 1) is almost reducible provided that the coefficients are analytic and close to …

In this paper we prove rigorous results on persistence of invariant tori and their whiskers.
The proofs are based on the parameterization method of [X. Cabré, E. Fontich, R. de la …

The paper also contains estimates on the amount of surviving tori. The worst situation
happens when the initial tori are normally elliptic. In this case, a torus (identified by the …

We eliminate by KAM methods the time dependence in a class of linear differential
equations in ℓ 2 subject to an unbounded, quasi-periodic forcing. This entails the pure-point …

This work focuses on quasi-periodic time-dependent perturbations of ordinary differential
equations near elliptic equilibrium points. This means studying ̇x=(A+εQ(t,ε))x+εg(t,ε)+h(x,t …