Georgia Institute of Technology College of Sciences

I will present a method for constructing periodic or quasi-periodic solutions for forced strongly dissipative systems. Our method applies to the varactor equation in electronic engineering and to the forced non-linear wave equation with a strong damping term proportional to the wave velocity. The strong damping leads to very few small divisors which allows to prove the existence by using a fixed point contraction theorem. The method also leads to efficient numerics. This is joint work with A. Celletti, L. Corsi, and R. de la Llave.