21 citations · 25 across the 5 of their papers we have counts for
6 papers
On some collinear configurations in the planar three-body problem
Alexei Tsygvintsev
In this paper, we further investigate the planar Newtonian three-body problem with a focus on collinear configurations, where either the three bodies or their velocities are aligne…
On the overfly algorithm in deep learning of neural networks
Alexei Tsygvintsev
In this paper we investigate the supervised backpropagation training of multilayer neural networks from a dynamical systems point of view. We discuss some links with the qualitativ…
Continued g-fractions and geometry of bounded analytic maps
Alexei Tsygvintsev
In this work we study qualitative properties of real analytic bounded maps. The main tool is approximation of real valued functions analytic in rectangular domains of the complex p…
On some exceptional cases in the integrability of the three-body problem
Alexei Tsygvintsev
We consider the Newtonian planar three--body problem with positive masses , , . We prove that it does not have an additional first integral meromorphic in the comple…
On the analytic non-integrability of the Rattleback problem
Holger R. Dullin, Alexei Tsygvintsev
We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodr…
On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations
Alexei Tsygvintsev
We consider systems of ordinary differential equations with quadratic homogeneous right hand side. We give a new simple proof of a result already obtained in [8,10] which gives the…