Closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\).

DOI10.1016/S0022-0396(03)00168-2zbMath1109.37048MaRDI QIDQ1419823

Yujun Dong, Long, Yiming

Publication date: 26 January 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemClosed characteristicIterated indexPartial symmetryPrescribed energy

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (20)

Minimal \(P\)-symmetric period problem of first-order autonomous Hamiltonian systems ⋮ Generalized Ambrosetti-Rabinowitz condition for minimal period solutions of autonomous Hamiltonian systems ⋮ Non-hyperbolic \(P\)-invariant closed characteristics on partially symmetric compact convex hypersurfaces ⋮ Retracted article: ``Minimal period symmetric solutions for some Hamiltonian systems via the Nehari manifold method ⋮ Subharmonic \(P^{l}\)-solutions of first order Hamiltonian systems ⋮ Multiple periodic solutions of Hamiltonian systems with prescribed energy ⋮ Higher \(P\)-symmetric Ekeland-Hofer capacities ⋮ Orbits with minimal period for a class of autonomous second order one-dimensional Hamiltonian systems ⋮ The existence of periodic solutions for second-order delay differential systems ⋮ Index iteration theories for periodic orbits: old and new ⋮ Multiple P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Stable P-symmetric closed characteristics on partially symmetric compact convex hypersurfaces ⋮ On the number of P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\) ⋮ Iteration inequalities of the Maslov \(P\)-index theory with applications ⋮ Stable closed characteristics on partially symmetric convex hypersurfaces ⋮ Indices and stability of the Lagrangian system on Riemannian manifold ⋮ Index iteration theory for symplectic paths and multiple periodic solution orbits ⋮ Multiplicity of closed characteristics on \(P\)-symmetric compact convex hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in \(\mathbb{R}^{2n} \) ⋮ Elliptic and non-hyperbolic closed characteristics on compact convex P-cyclic symmetric hypersurfaces in \(\mathbb{R}^{2n} \)

Cites Work

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• Convex Hamiltonian energy surfaces and their periodic trajectories
• Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
• Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
• Periodic orbits for convex hamiltonian systems
• The dynamics on three-dimensional strictly convex energy surfaces
• Hyperbolic closed characteristics on compact convex smooth hypersurfaces in \(\mathbb{R}^{2n}\)
• Bott formula of the Maslov-type index theory
• A Maslov-type index theory for symplectic paths
• Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics
• Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
• Index theory for symplectic paths with applications
• Morse theory and existence of periodic solutions of convex hamiltonian systems
• Periodic solutions of hamiltonian systems
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

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