Quasi-periodic solutions of nonlinear differential equations via the Floquet-Lin theory.

International audienceWe use a Floquet theory for quasi-periodic linear ordinary differential equations due to Zhensheng Lin to obtain results on the quasi-periodic solutions of quasi-periodic nonlinear ordinary differential equations. First we obtain an existence result, secondly we obtain on the continuous dependence by using a parametrized fixed point theorem, and thirdly we obtain a local result on the differentiable dependence by using an implicit function theorem in function spaces