2019
Том 71
№ 1

All Issues

Grechko A. L.

Articles: 3
Article (Ukrainian)

On some qualitative properties of monotone linear extensions of dynamical systems

Grechko A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 10. - pp. 1326-1335

We study monotone linear extensions of dynamical systems. The problem of existence of invariant manifolds and exponential separation is investigated for linear extensions on vector bundles that preserve the order structure. We also study the relationship between the monotonicity of linear extensions and the existence of bounded solutions of inhomogeneous linear extensions (weak regularity, quasiregularity).

Article (Ukrainian)

On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems

Grechko A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 604–611

We study sufficient conditions for the existence of bounded solutions of linear extensions of the dynamical systems.

Brief Communications (Ukrainian)

On necessary conditions for the weak regularity of a linear extension of a dynamical system on a torus

Grechko A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 3. - pp. 424–425

We give a necessary condition for the weak regularity of a linear extension of a dynamical system on a torus in the form of Fourier series with respect to a part of the variables.