Linear instability for periodic orbits of non-autonomous Lagrangian systems

DOI10.1088/1361-6544/abcb0bzbMath1456.58013arXiv1907.05864OpenAlexW3172254160MaRDI QIDQ5147941

Li Wu, Ran Yang, Alessandro Portaluri

Publication date: 29 January 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.05864

zbMATH Keywords

periodic orbitsspectral flowMaslov indexlinear instabilitynon-autonomous Lagrangian functions

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Lagrangian submanifolds; Maslov index (53D12) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Spectral flows (58J30)

Related Items (4)

Instability of closed orbits obtained by minimization* ⋮ Spectral flow, Brouwer degree and Hill's determinant formula ⋮ Linear instability of periodic orbits of free period Lagrangian systems ⋮ Sturm theory with applications in geometry and classical mechanics

Cites Work

• Unnamed Item
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• A \(K\)-theoretical invariant and bifurcation for homoclinics of Hamiltonian systems
• The homology of path spaces and Floer homology with conormal boundary conditions
• High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
• Morse index and the stability of closed geodesics
• Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit
• Spectral flow and bifurcation of critical points of strongly-indefinite functionals. I: General theory
• The Maslov index for paths
• Computation of the Maslov index and the spectral flow via partial signatures.
• Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point.
• Index theory for heteroclinic orbits of Hamiltonian systems
• Index theory for symplectic paths with applications
• Spectral flow, Maslov index and bifurcation of semi-Riemannian geodesics
• Maslov-type index theory for symplectic paths and spectral flow. II
• Maslov-type index theory for symplectic paths and spectral flow. I
• Linear instability of relative equilibria for \(n\)-body problems in the plane
• A dihedral Bott-type iteration formula and stability of symmetric periodic orbits
• A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
• Index theory for skew-adjoint Fredholm operators
• Bifurcation of heteroclinic orbits via an index theory
• Spectral flow, crossing forms and homoclinics of Hamiltonian systems
• The anti-integrable limit
• A smooth pseudo-gradient for the Lagrangian action functional
• On the maslov index
• Self-Adjoint Fredholm Operators And Spectral Flow
• Unbounded Fredholm Operators and Spectral Flow
• The Spectral Flow and the Maslov Index
• Morse index and bifurcation ofp-geodesics on semi Riemannian manifolds
• Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory

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