Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory

DOI10.1007/s00205-015-0898-2zbMath1395.70016arXiv1406.3519OpenAlexW3102833354MaRDI QIDQ5962864

Alessandro Portaluri, Vivina Barutello, Riccardo D. Jadanza

Publication date: 25 February 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.3519

Mathematics Subject Classification ID

Three-body problems (70F07) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Momentum maps; symplectic reduction (53D20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Index theory for dynamical systems, Morse-Conley indices (37B30)

Related Items (23)

Morse index and bifurcation for figure-eight choreographies of the equal mass three-body problem ⋮ Braids of the \(N\)-body problem. II: Carousel solutions by cabling central configurations ⋮ Linear stability of the criss-cross orbit in the equal-mass three-body problem ⋮ Spectral stability, spectral flow and circular relative equilibria for the Newtonian \(n\)-body problem ⋮ Linear stability of elliptic relative equilibria of restricted four-body problem ⋮ An index theory for asymptotic motions under singular potentials ⋮ Index theory for heteroclinic orbits of Hamiltonian systems ⋮ Spectral flow, Brouwer degree and Hill's determinant formula ⋮ Morse theory and relative equilibria in the planar \(n\)-vortex problem ⋮ Linear instability of periodic orbits of free period Lagrangian systems ⋮ Keplerian orbits through the Conley-Zehnder index ⋮ Sturm theory with applications in geometry and classical mechanics ⋮ Linear instability for periodic orbits of non-autonomous Lagrangian systems ⋮ On the sectional curvature along central configurations ⋮ Morse index for figure-eight choreographies of the planar equal mass three-body problem ⋮ Linear instability of relative equilibria for \(n\)-body problems in the plane ⋮ Morse index and stability of the planar \(N\)-vortex problem ⋮ Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions ⋮ On the stability of periodic N-body motions with the symmetry of Platonic polyhedra ⋮ Linear stability of the elliptic relative equilibrium with (1  +  n)-gon central configurations in planar n-body problem ⋮ On the minimality of Keplerian arcs with fixed negative energy ⋮ Instability of Periodic Orbits by Conley–Zehnder Index Theory ⋮ Instability of semi-Riemannian closed geodesics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory
• 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 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
• The structure of the singular symplectic matrix set
• Bott formula of the Maslov-type index theory
• The Maslov index for paths
• Computation of the Maslov index and the spectral flow via partial signatures.
• Corrigendum to: ``A Morse-Smale index theorem for indefinite elliptic systems and bifurcation
• Index theory for symplectic paths with applications
• Spectral flow, Maslov index and bifurcation of semi-Riemannian geodesics
• Noncollision periodic solutions to some singular dynamical systems with very weak forces
• Maslov-type index theory for symplectic paths and spectral flow. II
• Linear instability of relative equilibria for \(n\)-body problems in the plane
• A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
• Elliptic relative equilibria in the \(N\)-body problem
• Une caractérisation variationnelle des solutions de Lagrange du problème plan des trois corps
• On the iteration of closed geodesics and the sturm intersection theory
• On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients
• On a Generalized Sturm Theorem
• A Minimizing Property of Keplerian Orbits
• Minima de l'intégrale d'action et équilibres relatifs de n corps
• On the maslov index
• Action minimizing orbits in then-body problem with simple choreography constraint
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• A minimizing property of Lagrangian solutions

This page was built for publication: Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory