17 citations · 29 across the 9 of their papers we have counts for
9 papers
Dynamical bifurcation of multi-frequency oscillations in a fast-slow system
A. M. Samoilenko, I. O. Parasyuk, B. V. Repeta
We study a dynamical counterpart of bifurcation to invariant torus for a system of interconnected fast phase variables and slowly varying parameters. We show that in such a system,…
Frequency locking by external forcing in systems with rotational symmetry
Lutz Recke, Anatoly Samoilenko, Viktor Tkachenko +1
We study locking of the modulation frequency of a relative periodic orbit in a general -equivariant system of ordinary differential equations under an external forcing of modu…
On invariant manifolds of linear differential equations. II
A. M. Samoilenko
This is the continuation of previous article. For subspaces and which are invariant manifolds of the differential equation under consideration we build a chan…
On invariant manifolds of linear differential equations. I
A. M. Samoilenko
This article is the first in the cycle from two parts. It develops the ideas of integral manifolds method of M. M. Bogolubov in the case of linear differential equations in w…
Frequency locking of modulated waves
Lutz Recke, Anatoly Samoilenko, Alexey Teplinsky +2
We consider the behavior of a modulated wave solution to an -equivariant autonomous system of differential equations under an external forcing of modulated wave type.…
Local conservation laws of second-order evolution equations
Roman O. Popovych, Anatoly M. Samoilenko
Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78, 531-676], we completely describe local conservation laws of second-order (1+1)-dimensional evolution equati…