Том 70
№ 7

All Issues

Romanenko O. Yu.

Articles: 3
Anniversaries (Ukrainian)

Oleksandr Mykolaiovych Sharkovs’kyi (on his 80th birthday)

Fedorenko V. V., Ivanov А. F., Khusainov D. Ya., Kolyada S. F., Maistrenko Yu. L., Parasyuk I. O., Pelyukh G. P., Romanenko O. Yu., Samoilenko V. G., Shevchuk I. A., Sivak A. G., Tkachenko V. I., Trofimchuk S. I.

Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 257-260

Article (Ukrainian)

Self-stochasticity phenomenon in dynamical systems generated by difference equations with continuous argument

Romanenko O. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 7. - pp. 954–975

For dynamical systems generated by the difference equations x(t+1) = f(x(t)) with continuous time (f is a continuous mapping of an interval onto itself), we present a mathematical substantiation of the self-stochasticity phenomenon, according to which an attractor of a deterministic system contains random functions.

Article (Ukrainian)

Dynamics of solutions of the simplest nonlinear boundary-value problems

Romanenko O. Yu., Sharkovsky O. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 810–826

We investigate two classes of essentially nonlinear boundary-value problems by using methods of the theory of dynamical systems and two special metrics. We prove that, for boundary-value problems of both these classes, all solutions tend (in the first metric) to upper semicontinuous functions and, under sufficiently general conditions, the asymptotic behavior of almost every solution can be described (by using the second metric) by a certain stochastic process.