Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics
From MaRDI portal
Publication:1584527
DOI10.1006/aima.2000.1914zbMath0970.37013OpenAlexW2055444930MaRDI QIDQ1584527
Publication date: 15 October 2001
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/aima.2000.1914
Lagrangian submanifolds; Maslov index (53D12) Index theory for dynamical systems, Morse-Conley indices (37B30)
Related Items
Two elliptic closed geodesics on positively curved Finsler spheres ⋮ Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\) ⋮ Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics ⋮ Selected new aspects of the calculus of variations in the large ⋮ Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces ⋮ Resonance identity for symmetric closed characteristics on symmetric convex Hamiltonian energy hypersurfaces and its applications ⋮ Multiple closed geodesics on Riemannian 3-spheres ⋮ Multiple closed geodesics on bumpy Finsler \(n\)-spheres ⋮ Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\) under a pinching condition ⋮ The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form ⋮ The existence of two closed geodesics on every Finsler 2-sphere ⋮ Resonance identity and multiplicity of non-contractible closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ 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 \(\mathbf{R}^{2n}\) ⋮ Dynamical convexity and elliptic periodic orbits for Reeb flows ⋮ Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem ⋮ The irrational ratio of average indices of closed geodesics on positively curved Finsler spheres ⋮ Two closed geodesics on \(\mathbb RP^{2n+1}\) with a bumpy Finsler metric ⋮ Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory ⋮ Normal forms for symplectic matrices ⋮ Irrationally elliptic closed characteristics on symmetric compact convex hypersurfaces in \(\mathbb{R}^8\) ⋮ The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form \(S^{2n+1}/ \Gamma \) ⋮ Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond ⋮ Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics ⋮ Path integration over closed loops and Gutzwiller's trace formula ⋮ Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ On the average indices of closed geodesics on positively curved Finsler spheres ⋮ Beatty sequences and prime numbers with restrictions on strongly \(q\)-additive functions ⋮ Index iteration theories for periodic orbits: old and new ⋮ On a conjecture of Anosov ⋮ Closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\). ⋮ Closed geodesics on Finsler spheres ⋮ Multiple P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Closed geodesics on positively curved Finsler spheres ⋮ Stability of closed geodesics on Finsler 2-spheres ⋮ On a product formula for the Conley-Zehnder index of symplectic paths and its applications ⋮ Irrationally elliptic closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{2n}\) ⋮ The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds ⋮ Linear instability of elliptic rhombus solutions to the planar four-body problem ⋮ Irrationally elliptic closed characteristics on symmetric compact star-shaped hypersurfaces in \(\mathbf{R}^{4}\) ⋮ Stability of closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{2n}\) ⋮ Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem ⋮ Irrationally elliptic closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^6\) ⋮ Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres ⋮ Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions ⋮ Stable closed characteristics on partially symmetric convex hypersurfaces ⋮ Stability of Closed Characteristics on Compact Hypersurfaces in R2n Under a Pinching Condition ⋮ Linear stability of some symplectic matrices ⋮ Multiple brake orbits in bounded convex symmetric domains ⋮ Multiple closed geodesics on positively curved Finsler manifolds ⋮ Index iteration theory for symplectic paths and multiple periodic solution orbits ⋮ Closed Geodesics on Positively Curved Finsler 3-Spheres ⋮ Closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb R^{2n}\) ⋮ The index growth and multiplicity of closed geodesics ⋮ \( \omega^+\)-type index of \(\mathrm{GL}^+(2)\)-paths ⋮ Resonance identities for closed characteristics on compact star-shaped hypersurfaces in \(\mathbf R^{2n}\) ⋮ Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces ⋮ Closed characteristics on non-compact hypersurfaces in \(\mathbb {R}^{2n}\) ⋮ Elliptic and non-hyperbolic closed characteristics on compact convex P-cyclic symmetric hypersurfaces in \(\mathbb{R}^{2n} \) ⋮ Stability of closed characteristics on compact convex hypersurfaces in \(\mathbb R^{6}\) ⋮ Multiple closed geodesics on 3-spheres ⋮ The non-contractibility of closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ A review of the index method in closed geodesic problem ⋮ Multiplicity of closed Reeb orbits on dynamically convex \(\mathbb{R}P^{2n-1} \) for \(n\geq2\) ⋮ A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem ⋮ Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem ⋮ Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit ⋮ Symmetric closed characteristics on symmetric compact convex hypersurfaces in \(\mathbb{R}^8\) ⋮ The relation of the Morse index of closed geodesics with the Maslov-type index of symplectic paths ⋮ The Rabinowitz minimal periodic solution conjecture ⋮ 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 \(\mathbf{R}^{2n}\)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Une théorie de Morse pour les systèmes hamiltoniens convexes
- A new obstruction to embedding Lagrangian tori
- Convex Hamiltonian energy surfaces and their periodic trajectories
- On the average indices of closed geodesics
- Closed geodesics on positively curved manifolds
- The behavior of the index of a periodic linear Hamiltonian system under iteration
- Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
- Periodic orbits for convex hamiltonian systems
- Indexing domains of instability for Hamiltonian systems
- The dynamics on three-dimensional strictly convex energy surfaces
- Hyperbolic closed characteristics on compact convex smooth hypersurfaces in \(\mathbb{R}^{2n}\)
- Topological structures of \(\omega\)-subsets in symplectic groups
- Bott formula of the Maslov-type index theory
- The minimal period problem of classical Hamiltonian systems with even potentials
- The minimal period problem of periodic solutions for autonomous superquadratic second order Hamiltonian systems
- On the minimal period for the periodic solutions problem of nonlinear Hamiltonian systems
- A Maslov-type index theory for symplectic paths
- Hyperbolic characteristics on star-shaped hypersurfaces
- Multiple periodic points of the Poincaré map of Lagrangian systems on tori
- Maslov-type index theory for symplectic paths and spectral flow. II
- Maslov-type index theory for symplectic paths and spectral flow. I
- A generalized Sturm theorem
- On the iteration of closed geodesics and the sturm intersection theory
- New aspects in the theory of stability of Hamiltonian systems
- Equivariant Morse Theory for Starshaped Hamiltonian Systems
- Morse theory for periodic solutions of hamiltonian systems and the maslov index
- Periodic solutions of hamiltonian systems
- Hamiltonian systems with elliptic periodic orbits
- The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
- Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations