23 citations · 23 across the 6 of their papers we have counts for
6 papers · 1 filter
Poincaré map construction for some classical two predators - one prey systems
A V Osipov, G Söderbacka
In this paper we consider a family of system with 2 predators feeding on one prey. We show how to construct a positively invariant set in which it is possible to define a Poincaré…
Shadowing for differential equations with grow-up
Alexey Osipov
We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the poin…
Shadowing for actions of some finitely generated groups
Alexey Osipov, Sergey Tikhomirov
We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpote…
Inverse periodic shadowing properties
Alexey V. Osipov
We consider inverse periodic shadowing properties of discrete dynamical systems generated by diffeomorphisms of closed smooth manifolds. We show that the -interior of the set…
Nondensity of orbital shadowing property in C^1-topology
Alexey V. Osipov
The orbital shadowing property (OSP) of discrete dynamical systems on smooth closed manifolds is considered. Nondensity of OSP with respect to the C^1-topology is proved. The proof…
Periodic shadowing and -stability
Alexey Osipov, Sergei Yu. Pilyugin, Sergey Tikhomirov
We show that the following three properties of a diffeomorphism of a smooth closed manifold are equivalent: (i) belongs to the -interior of the set of diffeomorphisms…