Quantitative Stability of Certain Families of Periodic Solutions in the Sitnikov Problem

DOI10.1137/17M1113990zbMath1390.70017arXiv1612.07254OpenAlexW2583598081MaRDI QIDQ4608078

Andrés Rivera, Daniel E. Nuñez, Jorge E. Galán

Publication date: 15 March 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07254

zbMATH Keywords

Lyapunov stabilityimplicit function theoremelliptic periodic solutionsPoincaré's continuation method

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Three-body problems (70F07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (6)

Bifurcation of periodic orbits for the \(N\)-body problem, from a nongeometrical family of solutions ⋮ On the Stability of Symmetric Periodic Orbits of the Elliptic Sitnikov Problem ⋮ Stability and bifurcations of even periodic orbits in the Sitnikov problem ⋮ Unnamed Item ⋮ A Proof for a Stability Conjecture on Symmetric Periodic Solutions of the Elliptic Sitnikov Problem ⋮ On the stability of symmetric periodic solutions of the generalized elliptic Sitnikov \((N + 1)\)-body problem

Cites Work

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