9 citations · 11 across the 4 of their papers we have counts for
4 papers
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…
On the convergence of continued fractions at Runckel's points and the Ramanujan conjecture
Alexei Tsygvintsev
We consider the limit periodic continued fractions of Stieltjes $$ \frac{1}{1-} \frac{g_1 z}{1-} \frac{g_2(1-g_1) z}{1-} \frac{g_3(1-g_2)z}{1-...,}, z\in \mathbb C, g_i\in(0,1), \l…
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…
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…