7 papers
Uniform solvability for families of linear systems on time scales
Sergey Kryzhevich
We give explicit criteria of solvability for families of linear systems on time scales. We introduce a new method of embedding a time scale into a non-autonomous system of ODEs. Th…
Constructive controllability for incompressible vector fields
Sergey Kryzhevich, Eugene Stepanov
We give a constructive proof of a global controllability result for an autonomous system of ODEs guided by bounded locally Lipschitz and divergence free (i.e.\ incompressible) vect…
Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps
Sergey Kryzhevich, Viktor Avrutin, Nikita Begun +2
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties…
Inverse shadowing and related measures
Sergey Kryzhevich, Sergey Pilyugin
We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing…
Invariant measures for interval translations and some other piecewise continuous maps
Sergey Kryzhevich
We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the sim…
Hyperbolicity and solvability for linear systems on time scales
Sergey Kryzhevich
We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to…