8 papers · 1 filter
Countable IET Models and Defect Sets for Interval Translation Maps
Sergey Kryzhevich, Khosro Tajbakhsh, Reza Yaghmaeian
Interval translation maps are piecewise translations for which the images of distinct continuity intervals may overlap. We study when their measured dynamics can be represented by…
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…