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math.DS2024
Velocity Syzygies and Bounding Syzygy Moments in the Planar Three-Body Problem
Alexei Tsygvintsev
We consider the Newtonian planar three-body problem, defining a syzygy (velocity syzygy) as a configuration where the positions (velocities) of the three bodies become collinear. W…
math.DS2000
The meromorphic non-integrability of the three-body problem
Alexei Tsygvintsev
We study the planar three-body problem and prove the absence of a complete set of complex meromorphic first integrals in a neighborhood of the Lagrangian solution. We use the Zigli…
math.DS2000★ 9 cited
On the algebraic invariant curves of plane polynomial differential systems
Alexei Tsygvintsev
We consider a plane polynomial vector field of degree . To each algebraic invariant curve of such a field we associate a compact Riemann surface with the m…