Reducibility for the quasi-periodic linear Schrödinger and wave equations

Reducibility for the quasi-periodic linear Schrödinger and wave equations

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L. H. Eliasson, Université Paris Diderot
Fine Hall 601

We shall discuss reducibility of these equations on the torus with a small potential that depends quasi-periodically on time. Reducibility amounts to "reduce" the equation to a time-independent linear equation with pure point spectrum in which case all solutions will be of Floquet type. For the Schrödinger equation, this has been proven in a joint work with S. Kuksin, and for the wave equation we shall report on a work in progress with B. Grebert and S. Kuksin.