A proof of Weinstein's conjecture in \(\mathbb R^{2n}\)

DOI10.1016/S0294-1449(16)30363-8zbMath0631.58013WikidataQ60304902 ScholiaQ60304902MaRDI QIDQ1094714

Publication date: 1987

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1987__4_4_337_0

zbMATH Keywords

symplectic manifold characteristic existence of closed characteristics

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Global submanifolds (53C40) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Contact manifolds (general theory) (53D10)

Related Items

Linking and closed orbits, Existence of multiple periodic orbits of Hamiltonian systems on positive-type hypersurfaces in \({\mathbb{R}}^{2n}\), An algebraic approach to the algebraic Weinstein conjecture, Contact geometry in the restricted three-body problem: a survey, Basic facts and naive questions, On the number of periodic orbits of Hamiltonian systems on positive-type hypersurfaces in \(\mathbb{R}^{2n}\), Steady fluid flows and symplectic geometry, Relative Hofer-Zehnder capacity and periodic orbits in twisted cotangent bundles, Symplectic cobordisms and the strong Weinstein conjecture, Relative Hofer-Zehnder capacity and positive symplectic homology, Periodic solutions of Hamiltonian systems on hypersurfaces in a torus, Many closed \(K\)-magnetic geodesics on \(\mathbb{S}^2\), Periodic motions of conservative systems with singular potentials, The dimension of leaf closures of K-contact flows, On the Lebesgue measure of the periodic points of a contact manifold, An index theory and existence of multiple brake orbits for star-shaped Hamiltonian systems, Homoclinic orbits on compact hypersurfaces in \(\mathbb{R}^{2N}\), of restricted contact type, The brake orbits of Hamiltonian systems on positive-type hypersurfaces, On the topological properties of symplectic maps, The Weinstein conjecture in \(P\times {\mathbb{C}}^{\ell}\), A Viterbo-Hofer-Zehnder type result for hamiltonian inclusions, Closed orbits of Reeb fields on Sasakian manifolds and elliptic curves on Vaisman manifolds, Multiple periodic solutions of Hamiltonian systems with prescribed energy, Computing the Rabinowitz Floer homology of tentacular hyperboloids, Three constructions in symplectic topology, Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications, A remark on unique ergodicity and the contact type condition, \(b\)-contact structures on tentacular hyperboloids, Periodic orbits in virtually contact structures, Contact Open Books and Symplectic Lefschetz Fibrations (Survey), On symplectic uniruling of Hamiltonian fibrations, Relative periodic solutions of the \(N\)-vortex problem via the variational method, The sharp energy-capacity inequality on convex symplectic manifolds, Weinstein conjecture and a theory of infinite dimensional cycles, Coisotropic intersections, Extended Fuller index, sky catastrophes and the Seifert conjecture, Periodic solutions for a prescribed-energy problem of singular Hamiltonian systems, Closed characteristics on singular energy levels of second-order Lagrangian systems, Recent advances in symplectic flexibility, Existence of periodic solutions of Hamiltonian systems on almost every energy surface, Noncontractible periodic orbits in cotangent bundles and Floer homology, Floer homologies, with applications, On the existence and non-existence of closed trajectories for some Hamiltonian flows, Closed characteristics on non-compact hypersurfaces in \(\mathbb {R}^{2n}\), Remarks about the \(C^{\infty }\)-closing lemma for 3-dimensional Reeb flows, A prescribed-energy problem for a conservative singular Hamiltonian system, A survey of symplectic and contact topology, Unnamed Item, Taubes’s proof of the Weinstein conjecture in dimension three, Applications of convex integration to symplectic and contact geometry, Symplectic topology and Hamiltonian dynamics. II, Almost existence from the feral perspective and some questions, Mechanical Hamiltonian systems with respect to linear Poisson structures and Jacobi-Reeb dynamics, The compact category and multiple periodic solutions of Hamiltonian systems on symmetric starshaped energy surfaces, On contact type hypersurfaces in 4-space

Cites Work