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

Joël Blot (1) , Jihed Ben Slimene (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

We 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.

Mots clés: quasi-periodic functions; Floquet theory; fixed point theorem; implicit function theorem.; implicit function theorem

Domaines: Systèmes dynamiques [math.DS]

Joël Blot, Jihed Ben Slimene. Quasi-periodic solutions of nonlinear differential equations via the Floquet-Lin theory.. Differential Equations and Applications, 2010, 2 (3), pp.331-343. ⟨hal-00662551⟩