Vlasenko I. Yu.
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.
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.
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.
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.
Numerical Characteristics on the Set of Heteroclinic Points of Morse–Smale Diffeomorphisms on Surfaces
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.