48 citations · 97 across the 10 of their papers we have counts for
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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…