Periodic Solutions in the Generalized Sitnikov $(N+1)$-Body Problem

DOI10.1137/120883876zbMath1282.70017OpenAlexW2018953021MaRDI QIDQ2871370

Andrés Rivera

Publication date: 22 January 2014

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

Full work available at URL: https://doi.org/10.1137/120883876

zbMATH Keywords

periodic orbitsbifurcations\(N\)-body problemSitnikov problemglobal continuationSturm-Liouville theory

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 (10)

Bifurcation of periodic orbits for the \(N\)-body problem, from a nongeometrical family of solutions ⋮ On the global families of periodic solutions of a generalized Sitnikov problem ⋮ Symmetric periodic solutions in the Sitnikov problem ⋮ Periodic oscillations in the restricted hip-hop \(2N+1\)-body problem ⋮ Quantitative Stability of Certain Families of Periodic Solutions in the Sitnikov Problem ⋮ Unnamed Item ⋮ The Sitnikov problem for several primary bodies configurations ⋮ Resonance tongues in the linear Sitnikov equation ⋮ Periodic solutions of a generalized Sitnikov problem ⋮ On the stability of symmetric periodic solutions of the generalized elliptic Sitnikov \((N + 1)\)-body problem

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