Basic bifurcation scenarios in neighborhoods of boundaries of stability regions of libration points in the three-body problem

DOI10.1007/s10958-019-04430-7zbMath1455.70007OpenAlexW2966551530MaRDI QIDQ2278256

M. G. Yumagulov

Publication date: 4 December 2019

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-019-04430-7

zbMATH Keywords

stabilityperiodic solutionsthree-body problembifurcationparameterstability regionlibration point

Mathematics Subject Classification ID

Three-body problems (70F07) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Bifurcations of singular points in dynamical systems (37G10) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Cites Work

• Construction of stability regions in the three-body problem using parameter elimination
• Stability sets of multiparameter Hamiltonian systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Linear stability of the elliptic Lagrangian triangle solutions in the three-body problem
• Bifurcations of periodic solutions near triangular libration points in the three-body problem
• Periodic solutions of the restricted three-body problem for a small mass ratio
• Stability Regions of Nonlinear Dynamical Systems
• Stability of the triangular points in the elliptic restricted problem of three bodies
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