Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond
DOI10.1016/j.jfa.2024.110352arXiv2205.07082MaRDI QIDQ6119961
Long, Yiming, Hui Liu, Wei Wang, Hua Gui Duan
Publication date: 20 February 2024
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2205.07082
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Periodic solutions to ordinary differential equations (34C25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Geodesics in global differential geometry (53C22) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)
Cites Work
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- The existence of two closed characteristics on every compact star-shaped hypersurface in \(\mathbb{R}^{4}\)
- Existence of closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{2n}\)
- Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\)
- Closed Reeb orbits on the sphere and symplectically degenerate maxima
- On the minimal number of periodic orbits on some hypersurfaces in \(\mathbb{R}^{2n}\)
- The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds
- Multiplicity of periodic orbits for dynamically convex contact forms
- Homology generated by iterated closed geodesics
- Multiplicity of closed characteristics on symmetric convex hypersurfaces in \(\mathbb{R}^{2n}\)
- Stability of closed characteristics on compact convex hypersurfaces in \(\mathbb R^{6}\)
- Multiple orbits for Hamiltonian systems on starshaped surfaces with symmetries
- Multiplicité des trajectoires fermées de systèmes hamiltoniens connexes. (Multiplicity of closed trajectories of convex Hamiltonian systems)
- Convex Hamiltonian energy surfaces and their periodic trajectories
- 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
- Finite energy foliations of tight three-spheres and Hamiltonian dynamics
- Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics
- Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
- Multiplicity of closed Reeb orbits on prequantization bundles
- Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb{R}^{2n}\)
- Infinite dimensional Morse theory and multiple solution problems
- Index theory for symplectic paths with applications
- Hyperbolic characteristics on star-shaped hypersurfaces
- Dynamical convexity and closed orbits on symmetric spheres
- A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem
- Lusternik-Schnirelmann theory and closed Reeb orbits
- Torsion contact forms in three dimensions have two or infinitely many Reeb orbits
- Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces
- Closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb R^{2n}\)
- Resonance identities for closed characteristics on compact star-shaped hypersurfaces in \(\mathbf R^{2n}\)
- Existence of multiple periodic orbits on star‐shaped hamiltonian surfaces
- Morse theory and existence of periodic solutions of convex hamiltonian systems
- Equivariant Morse Theory for Starshaped Hamiltonian Systems
- Periodic solutions of hamiltonian systems
- S1-Equivariant Symplectic Homology and Linearized Contact Homology
- Local contact homology and applications
- Iterated index and the mean Euler characteristic
- Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces
- From one Reeb orbit to two
- Contact three-manifolds with exactly two simple Reeb orbits
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