1 citations · 5 across the 9 of their papers we have counts for
9 papers
On asymptotic phase of dynamical system hyperbolic along attracting invariant manifold
Alina Luchko, Igor Parasyuk
We consider a dynamical system which has the hyperbolic structure along an attracting invariant manifold . The problem is whether every motion starting in a neighborhood of …
A counterpart of Landau -- Hadamard type inequality for manifold-valued mappings
Igor Parasyuk
We obtain a Landau -- Hadamard type inequality for mappings defined on the whole real axis and taking values in Riemannian manifolds. In terms of an auxiliary convex function, we f…
Hyperbolic quasiperiodic solutions of U-monotone systems on Riemannian manifolds
Igor Parasyuk
We consider a second order non-autonomous system which can be interpreted as the Newtonian equation of motion on a Riemannian manifold under the action of time-quasiperiodic force…
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,…
Existence theorem for hyperbolic quasiperiodic solutions of Lagrangian systems on Riemannian manifolds
Igor Parasyuk
We establish new sufficient conditions for the existence of classical hyperbolic quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodi…
Existence theorem for weak quasiperiodic solutions of Lagrangian systems on Riemannian manifolds
Igor Parasyuk, Anna Rustamova
We establish new sufficient conditions for the existence of weak Besicovitch quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodic fo…