Vereikina M. B.
Ukr. Mat. Zh. - 1997. - 49, № 8. - pp. 1016–1024
We investigate properties of dynamical systems associated with the approximation of pseudotrajectories of a dynamical system by its trajectories. According to modern terminology, a property of this sort is called the “property of tracing pseudotrajectories” (also known in the English literature as the “shadowing property”). We prove that dynamical systems given by mappings of a compact set into itself and possessing this property are systems with stable prolongation of orbits. We construct examples of mappings of an interval into itself that prove that the inverse statement is not true, i.e., that dynamical systems with stable prolongation of orbits may not possess the property of tracing pseudotrajectories.
Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1398–1410
The article presents three scenarios of the evolution of spatial-temporal chaos and specifies the corresponding types of chaotic solutions to a certain nonlinear boundary-value problem for PDE. Analytic assertions are illustrated by numerical analysis and computer graphics.