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Construction of quasi-periodic response solutions for forced systems with damping

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Construction of quasi-periodic response solutions for forced systems with damping
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Construction of quasi-periodic response solutions for forced systems with strong damping
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22
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
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I will present a method for constructing quasi-periodic response solutions (i.e. quasi-periodic solutions with the same frequency as the forcing) for over-damped systems. Our method applies to non-linear wave equations subject to very strong damping and quasi-periodic external forcing and to the varactor equation in electronic engineering. The strong damping leads to very few small divisors which allows to prove the existence by using a contraction mapping argument requiring very weak non-resonance conditions on the frequency. This is joint work with A. Celletti, L. Corsi, and R. de la Llave.