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Fast oscillating forced systems: reducibility for a linear Klein-Gordon equation

Luca Franzoi
Friday, November 16, 2018 - 14:00

Aim of this talk is to show a reducibility result for a linear Klein-Gordon equation on a one dimensional compact interval, whose dynamics is subject to an external forcing potential that depends quasiperiodically on time. The size of the latter is not necessarily small, and so this is not a perturbative result. Nevertheless, reducibility is achieved by taking the frequency vector of the potential sufficiently large.

In the first half of the talk I will briefly review some features of fast driven systems, Floquet theory in infinite dimension and the problem of the growth of the Sobolev norms, in order to present the main result and its corollaries.
In the second half I will focus on the two main novel points of the proof: the use of pseudodifferential operators for performing one step of Magnus normal form, which recovers a perturbative setting; the structure of the nonresonant conditions needed for a following KAM reduction scheme. If time permits, I will say some words on what happens when one considers different equations, rather than the Klein-Gordon one.

This is a joint work with Alberto Maspero.

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