Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\)

DOI10.1016/j.aim.2016.03.044zbMath1341.52010arXiv1305.4680OpenAlexW2964204261MaRDI QIDQ284862

Wei Wang

Publication date: 18 May 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4680

zbMATH Keywords

Morse theoryHamiltonian systemsindex iteration theoryclosed characteristicscompact convex hypersurfacesFloquet multiplicity

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (15)

Multiplicity of closed Reeb orbits on prequantization bundles ⋮ Non-hyperbolic \(P\)-invariant closed characteristics on partially symmetric compact convex hypersurfaces ⋮ Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in \(\mathbb R^{2n}\) ⋮ A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in \(\mathbf{R}^{2n}\) ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ Irrationally elliptic closed characteristics on symmetric compact convex hypersurfaces in \(\mathbb{R}^8\) ⋮ Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond ⋮ Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Index iteration theories for periodic orbits: old and new ⋮ Irrationally elliptic closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{2n}\) ⋮ Irrationally elliptic closed characteristics on symmetric compact star-shaped hypersurfaces in \(\mathbf{R}^{4}\) ⋮ 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 \(\mathbb{R}^{2n} \) ⋮ Multiplicity of closed Reeb orbits on dynamically convex \(\mathbb{R}P^{2n-1} \) for \(n\geq2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Une théorie de Morse pour les systèmes hamiltoniens convexes
• A new obstruction to embedding Lagrangian tori
• Stability of closed characteristics on compact convex hypersurfaces in \(\mathbb R^{6}\)
• Convex Hamiltonian energy surfaces and their periodic trajectories
• On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface
• Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
• Critical point theory and 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
• Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics
• Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
• Infinite dimensional Morse theory and multiple solution problems
• Index theory for symplectic paths with applications
• Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces
• On differentiable functions with isolated critical points
• Normal modes for nonlinear Hamiltonian systems
• 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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