48 citations · 97 across the 10 of their papers we have counts for
11 papers
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…
Nonsmooth mappings with Lipschitz shadowing
A. Petrov, S. Pilyugin
We study conditions under which a piecewise affine mapping has the Lipschitz shadowing property. As an application, we show that there exists a homeomorphism with a nonisolated fix…
Multidimensional transversality
Aleksey A. Petrov, Sergei Yu. Pilyugin
In 1994, Sakai introduced the property of transversality for two smooth curves in a two-dimensional manifold. This property was related to various shadowing properties of dyn…
Lyapunov functions, shadowing, and topological stability
Alexey A. Petrov, Sergei Yu. Pilyugin
We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish th…
Shadowing near nonhyperbolic fixed points
Alexey A. Petrov, Sergei Yu. Pilyugin
We use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diff…
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…