48 citations · 94 across the 5 of their papers we have counts for
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Lipschitz Shadowing for Flows
Kennet J. Palmer, Sergei Pilyugin, Sergey Tikhomirov
Let be the flow generated by a smooth vector field on a smooth closed manifold. We show that the Lipschitz shadowing property of is equivalent to the structural stabili…
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…