Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem

DOI10.1007/s00205-017-1154-8zbMath1382.35293arXiv1510.06822OpenAlexW2223847996MaRDI QIDQ1683790

Long, Yiming, Qing-Long Zhou

Publication date: 1 December 2017

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

Full work available at URL: https://arxiv.org/abs/1510.06822

zbMATH Keywords

linear stability separation curveslinearized Hamiltonean systemMaslov-type \(\omega\) indicesthree-body elliptic Euler problem

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Three-body problems (70F07) Lagrangian submanifolds; Maslov index (53D12) PDEs in connection with mechanics of particles and systems of particles (35Q70)

Related Items (12)

The reduction of the linear stability of elliptic Euler-Moulton solutions of the \(n\)-body problem to those of 3-body problems ⋮ Linear stability of elliptic relative equilibria of restricted four-body problem ⋮ Hill-type formula for Hamiltonian system with Lagrangian boundary conditions ⋮ Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem ⋮ Linear stability of elliptic relative equilibria of four-body problem with two infinitesimal masses ⋮ Linear stability of an elliptic relative equilibrium in the spatial \(n\)-body problem via index theory ⋮ Index iteration theories for periodic orbits: old and new ⋮ Trace estimation of a family of periodic Sturm-Liouville operators with application to Robe’s restricted three-body problem ⋮ Linear instability of elliptic rhombus solutions to the planar four-body problem ⋮ Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem ⋮ Collision index and stability of elliptic relative equilibria in planar \(n\)-body problem ⋮ Linear stability of the elliptic relative equilibrium with (1  +  n)-gon central configurations in planar n-body problem

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