Réductibilité et théorie de Floquet pour des systèmes différenciels non linéaires

Abstract : We use a Floquet theory for quasi-periodic linear ordinary differential equations due to Zhensheng Lin to obtain results, of existence, unicity, continuous and differentiable dependence, on the quasi-periodic solutions of quasi-periodic nonlinear ordinary differential equations. in a second time we establish the reducibility of linear systems of almost periodic differential equations into upper triangular systems of a.p. differential equations. This is done while the number of independent a. p. solutions is conserved. We prove existence and uniqueness of a. p. solutions of a nonlinear system with an a.p. linear part. Also we prove the continuous dependence of a.p. solutions of a nonlinear system with respect to an a.p. control term.
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Jihed Ben Slimene. Réductibilité et théorie de Floquet pour des systèmes différenciels non linéaires. Systèmes dynamiques [math.DS]. Université Panthéon-Sorbonne - Paris I, 2013. Français. ⟨tel-00952406⟩

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