Heteroclinic connections between periodic orbits in planar restricted circular three body problem. II

DOI10.1007/s00220-005-1374-xzbMath1133.70005arXivmath/0401146OpenAlexW3104136855MaRDI QIDQ818594

Daniel Wilczak, Piotr Zgliczyński

Publication date: 21 March 2006

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0401146

Mathematics Subject Classification ID

Three-body problems (70F07) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (18)

A note on the existence of a Smale horseshoe in the planar circular restricted three-body problem ⋮ Parameterization method for unstable manifolds of delay differential equations ⋮ Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model ⋮ Computer assisted proof of homoclinic chaos in the spatial equilateral restricted four-body problem ⋮ Infinitely Many Heteroclinic Orbits of a Complex Lorenz System ⋮ Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method ⋮ Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems ⋮ Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP ⋮ The use of invariant manifolds for transfers between unstable periodic orbits of different energies ⋮ Torus knot choreographies in the n-body problem ⋮ Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields ⋮ Automatic differentiation for Fourier series and the radii polynomial approach ⋮ Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence ⋮ A computer-assisted proof of symbolic dynamics in Hyperion's rotation ⋮ Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System ⋮ CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems ⋮ On Singular Orbits and Global Exponential Attractive Set of a Lorenz-Type System ⋮ A THREE-DIMENSIONAL NONLINEAR SYSTEM WITH A SINGLE HETEROCLINIC TRAJECTORY

Uses Software

• CAPD

Cites Work

• Reversing \(k\)-symmetries in dynamical systems
• Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof
• Chaos in the Kuramoto-Sivashinsky equations -- a computer-assisted proof.
• Topological method for symmetric periodic orbits for maps with a reversing symmetry
• Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Hénon map
• On the generalization of a theorem of A. Liapounoff
• Reversing symmetries in dynamical systems
• Possible chaotic motion of comets in the Sun–Jupiter system—a computer-assisted approach based on shadowing
• Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
• Symmetric Heteroclinic Connections in the Michelson System: A Computer Assisted Proof

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