2019
Том 71
№ 11

All Issues

Vlasenko I. Yu.

Articles: 5
Article (Russian)

An Example of Neutrally Nonwandering Points for the Inner Mappings that are Not Neutrally Recurrent

Vlasenko I. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1030-1033

In the previous papers, the author offered a new theory of topological invariants for the dynamical systems formed by noninvertible inner mappings. These invariants are constructed by using the analogy between the trajectories of homeomorphisms and directions in the set of points with common iteration. In particular, we introduce the sets of neutrally recurrent and neutrally nonwandering points. We also present an example of the so-called “neutrally nonwandering but not neutrally recurrent” points, which shows that these sets do not coincide.

Brief Communications (English)

On iteration stability of the Birkhoff center with respect to power 2

Polulyakh E. O., Vlasenko I. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 5. - pp. 705–707

It is proved that the Birkhoff center of a homeomorphism on an arbitrary metric space coincides with the Birkhoff center of its power 2.

Article (Russian)

Topological Properties of Periodic Components of Structurally Stable Diffeomorphisms

Vlasenko I. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1190-1199

We consider periodic components of structurally stable diffeomorphisms on two-dimensional manifolds. We study properties of these components and give a topological description of their boundaries.

Article (Russian)

Topological Properties of Periodic Components of A-Diffeomorphisms

Vlasenko I. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1031-1041

We consider periodic components of A-diffeomorphisms on two-dimensional manifolds. We study properties of these components and give a topological description of their boundaries.

Brief Communications (Ukrainian)

Numerical Characteristics on the Set of Heteroclinic Points of Morse–Smale Diffeomorphisms on Surfaces

Vlasenko I. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1415-1420

For Morse–Smale diffeomorphisms on closed surfaces, we investigate the properties of numerical characteristics of heteroclinic trajectories with respect to the local structure of direct product in a small neighborhood of a saddle periodic point.