48 citations · 178 across the 24 of their papers we have counts for
6 papers · 1 filter
Symmetric periodic solutions of parabolic problems with hysteresis
Pavel Gurevich, Sergey Tikhomirov
We consider the heat equation in a multidimensional domain with nonlocal hysteresis feedback control in a boundary condition. Thermostat is our prototype model. We construct all pe…
Lipschitz shadowing implies structural stability
Sergei Yu. Pilyugin, Sergey Tikhomirov
We show that the Lipschitz shadowing property of a diffeomorphism is equivalent to structural stability. As a corollary, we show that an expansive diffeomorphism having the Lipschi…
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…
Vector Fields with the Oriented Shadowing Property
Sergei Yu. Pilyugin, Sergey Tikhomirov
We give a description of the $\Cone$-interior ($\Int^1(\OrientSh)$) of the set of smooth vector fields on a smooth closed manifold that have the oriented shadowing property. A spec…
Sets of vector fields with various properties of shadowing of pseudotra-jectories
Sergei Yu. Pilyugin, Sergey Tikhomirov
We study the structure of -interiors of sets of smooth vector fields with various properties of shadowing of pseudotrajectories. It is shown for which classes of reparametriza…
Interiors of sets of vector fields with shadowing corresponding to certain classes of reparameterizations
Sergey Tikhomirov
We study -interiors of sets of vector fields with various shadowing properties. For the case of Lipschitz shadowing property the -interior equals the set of structurally…