One-dimensional three-body problem via symbolic dynamics

DOI10.1063/1.1287064zbMath0988.70008OpenAlexW2012663461WikidataQ47870322 ScholiaQ47870322MaRDI QIDQ2726381

Seppo Mikkola, Kiyotaka Tanikawa

Publication date: 17 July 2001

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/503bbc1de206b0bfdc56f31a84cbd3e42efd4fb4

zbMATH Keywords

Cantor setsymbolic dynamicsPoincaré sectionbinary collisionsone-dimensional three-body problemadmissible symbol sequencesinadmissible sequences of collisionsinfinity of periodic orbits

Mathematics Subject Classification ID

Three-body problems (70F07) Dynamical systems in classical and celestial mechanics (37N05) Collisions in celestial mechanics, regularization (70F16)

Related Items (12)

The rectilinear three-body problem using symbol sequence. I: Role of triple collision ⋮ Triple collision orbits with nonzero initial velocities ⋮ On ``generalized Kepler's third law and mass dependence of periods of three-body orbits ⋮ Non-Schubart periodic orbits in the rectilinear three-body problem ⋮ Periodic orbits and binary collisions in the classical three-body Coulomb problem ⋮ Reversible maps in two-degrees of freedom Hamiltonian systems ⋮ Ejection-collision orbits in two degrees of freedom problems in celestial mechanics ⋮ The rectilinear three-body problem ⋮ A search for triple collision orbits inside the domain of the free-fall three-body problem ⋮ From brake to syzygy ⋮ The rectilinear three-body problem using symbol sequence. II: Role of the periodic orbits ⋮ Numerical experiments of the planar equal-mass three-body problem: The effects of rotation

Cites Work

• A numerical investigation of the one-dimensional Newtonian three-body problem. II: Positive energies
• A numerical investigation of the one-dimensional Newtonian three-body problem
• Oscillatory orbits in the planar three-body problem with equal masses
• Triple collisions in the one-dimensional three-body problem
• Numerical treatment of ordinary differential equations by extrapolation methods
• Numerische Aufsuchung periodischer Lösungen im Dreikörperproblem
• Order and chaos in the planar isosceles three-body problem

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