TY - Type of reference TI - Ensembles limites et dynamique globale pour les 2-D champs de vecteurs sans divergence AU - Habib Marzougui AB - The global structure of divergence-free vector fields on closed surfaces is investigated. We prove that if M is a closed surface and $$${V}$$$ is a divergence-free $$$C^{1}$$$-vector field with finitely many singularities on M then every orbit L of $$$\mathcal{V}$$$ is one of the following types : (i) a singular point, (ii) a periodic orbit, (iii) a closed (non periodic) orbit in M* = M - Sing($$$\mathcal{V}$$$), (iv) a locally dense orbit, where Sing($$$\mathcal{V}$$$) denotes the set of singular points of $$$\mathcal{V}$$$. On the other hand, we show that the complementary in M of periodic components and minimal components is a compact invariant subset consisting of singularities and closed (non compact) orbits in M*. These results extend those of T. Ma and S. Wang in [Discrete Contin. Dynam. Systems, 7 (2001), 431-445] established when the divergence-free vector field $$$\mathcal{V}$$$ is regular that is all its singular points are non-degenerate. DO - 10.21494/ISTE.OP.2022.0837 JF - Avancées en Mathématiques Pures et Appliquées KW - divergence free-vector -elds, quasiminimal set,  !-limit set, non- trivial recurrent orbit, Poincar-e-Bendixson Theorem, minimal component, closed surface, divergence free-vector -elds, quasiminimal set, !-limit set, non- trivial recurrent orbit, Poincar-e-Bendixson Theorem, minimal component, closed surface, L1 - https://openscience.fr/IMG/pdf/iste_apam22v13n3_1.pdf LA - fr PB - ISTE OpenScience DA - 2022/06/1er SN - 1869-6090 TT - Limit sets and global dynamic for 2-D divergence-free vector fields UR - https://openscience.fr/Ensembles-limites-et-dynamique-globale-pour-les-2-D-champs-de-vecteurs-sans IS - Numéro 3 (Juin 2022) VL - 13 ER -