35 citations · 39 across the 19 of their papers we have counts for
23 papers
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…
Bounded and exponentially decaying solutions of almost linear dynamic systems on time scales
Svetlin Georgiev, Sergey Kryzhevich
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For -differential operators, corresponding…
Linear Time-Varying Dynamic-Algebraic Equations of Index on Time Scales
Svetlin Georgiev, Sergey Kryzhevich
In this paper, we introduce a class of linear time-varying dynamic-algebraic equations(LTVDAE) of tractability index on arbitrary time scales. We propose a procedure for t…
Linear Time-Varying Dynamic-Algebraic Equations of Index One on Time Scales
Svetlin G. Georgiev, Sergey Kryzhevich
In this paper, we introduce a class of linear time-varying dynamic-algebraic equations(LTVDAE) of tractability index one on arbitrary time scales. We propose a procedure for the de…
Rotating rod and ball
Sergey Kryzhevich, Alexander Plakhov
We consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The…
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…
The saga of a fish: from a survival guide to closing lemmas
Sergey Kryzhevich, Eugene Stepanov
In the paper by D.~Burago, S.~Ivanov and A.~Novikov, "A survival guide for feeble fish", it has been shown that a fish with limited velocity can reach any point in the (possibly un…
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…
Sets of invariant measures and Cesaro stability
Sergey Kryzhevich
Sets of invariant measures are considered for continuous maps of a metric compact set. We take Kantorovich metric to calculate distance between measures and Hausdorff metrics to ca…
Stability by linear approximation for time scale dynamical systems
Sergey Kryzhevich, Alexander Nazarov
We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear pertu…
Multishadowing in topological dynamics
Danila Cherkashin, Sergey Kryzhevich
An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small er…
On the Plaque Expansivity Conjecture
Sergey Kryzhevich
It is one of the main properties of uniformly hyperbolic dynamics that points of two distinct trajectories cannot be uniformly close one to another. This characteristics of hyperbo…
Motion of a rough disc in Newtonian aerodynamics
Sergey Kryzhevich
Dynamics of rough discs in a rarified media is considered. We study possible trajectories of centers of discs. The main result of the paper is the following: any finite rectifiable…
One-dimensional chaos in a system with dry friction: analytical approach
Nikita Begun, Sergey Kryzhevich
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction…
Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points
Sergey Kryzhevich, Sergei Pilyugin
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodi…
Through the Looking-Glass of the Grazing Bifurcation: Part I - Theoretical framework
James Ing, Sergey Kryzhevich, Marian Wiercigroch
It is well-known for vibro-impact systems that the existence of a periodic solution with a low-velocity impact (so-called grazing) may yield complex behavior of the solutions. In t…
Partial hyperbolicity and central shadowing
Sergey Kryzhevich, Sergey Tikhomirov
We study shadowing property for a partially hyperbolic diffeomorphism . It is proved that if is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotra…
Smale Horseshoe and Grazing Bifurcation in Impact Systems
Sergey Kryzhevich
Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the…
Topology of Vibro-Impact Systems in the Neighborhood of Grazing
Sergey Kryzhevich, Marian Wiercigroch
The grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for existence of a grazing family of periodic so…