Solutions périodiques de systèmes différentiels périodiques de dimension trois avec symétries

Abstract : This work studies periodics differentiel systems, in third dimension with symmetries. We look for periodic solutions of systems of this kind. We study definitions and properties for systems and their solutions we prove that every periodic system with symmetries has always a non trivial periodic solution, with the symmetries of the systems. We use theses results to give a new method called "symmetries method" to answer to the problem of existence of periodic solutions for differential systems perturbated in a critical way with symmetries. In the critical case, Poincaré's theorem cannot be applied to prove existence of periodic solutions for the perturbated systems. The "symmetries method" give results where another methods are fruitless, either because of complicated computations (J.K. Hale) or for reasons of inapplicability (Malkin) the "symmetries method" can provide in some cases existence of periodic solutions for non linear differential systems with symmetries expressed by x = Bx + G(t, x) where G has an affine or linear majoration. It osknow that kind of systems are difficults to study
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Mohamed Kurdi. Solutions périodiques de systèmes différentiels périodiques de dimension trois avec symétries. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1987. Français. ⟨NNT : 1987METZ003S⟩. ⟨tel-01775523⟩

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