Chaotic instability in three-body problem

DOI10.1007/BF01176373zbMath0602.70012OpenAlexW2092222834MaRDI QIDQ1082097

Michail Zak

Publication date: 1986

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01176373

zbMATH Keywords

geodesic flowchaotic behaviorexponential instabilityplane three body problemtwo dimensional compact manifold of negative Gaussian curvature

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Three-body problems (70F07) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Cites Work

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• Deterministic representation of chaos in classical dynamics.
• Two types of chaos in nonlinear mechanics
• On the ultimate behavior of orbits with respect to an unstable critical point. I: Oscillating, asymptotic, and capture orbits
• Low Energy Transit Orbits in the Restricted Three-Body Problems
• QUASIRANDOM DYNAMICAL SYSTEMS. I. QUASIRANDOM DIFFEOMORPHISMS
• Isolated Invariant Sets and Isolating Blocks

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