Some Collision Solutions of the Rectilinear Periodically Forced Kepler Problem

DOI10.1515/ans-2015-5021zbMath1336.37050OpenAlexW2471880825MaRDI QIDQ2789495

Lei Zhao

Publication date: 1 March 2016

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-624263

zbMATH Keywords

quasi-periodic solutionsKAM theorycelestial mechanics

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Collisions in celestial mechanics, regularization (70F16)

Related Items (10)

Periodic linear motions with multiple collisions in a forced Kepler type problem ⋮ Shooting for collinear periodic orbits in the Helium model ⋮ The extended Lissajous-Levi-Civita transformation ⋮ Generalized periodic orbits of the time-periodically forced Kepler problem accumulating at the center and of circular and elliptic restricted three-body problems ⋮ The Lissajous-Kustaanheimo-Stiefel transformation ⋮ Regularized variational principles for the perturbed Kepler problem ⋮ Generalized periodic orbits in some restricted three-body problems ⋮ Periodic solutions to a forced Kepler problem in the plane ⋮ Periodic solutions and regularization of a Kepler problem with time-dependent perturbation ⋮ Periodic bouncing solutions of the Lazer-Solimini equation with weak repulsive singularity

Cites Work

• Unnamed Item
• Linear motions in a periodically forced Kepler problem
• Invariant tori in Hamiltonian systems with two degrees of freedom in a neighborhood of a resonance
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• On Periodic Solutions of Nonlinear Differential Equations with Singularities

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