S. Tikhomirov

activity

20102026

most citedLipschitz shadowing implies structural stability

48 citations · 178 across the 24 of their papers we have counts for

collaborators

Showing 2011 · math.DSShow all

3 papers · 2 filters

math.DS2011

Partial hyperbolicity and central shadowing

Sergey Kryzhevich, Sergey Tikhomirov

We study shadowing property for a partially hyperbolic diffeomorphism $f$ . It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotra…

math.DS2011★ 18 cited

Holder Shadowing on Finite Intervals

Sergey Tikhomirov

For any $θ, ω > 1/2$ we prove that, if any $d$ -pseudotrajectory of length $\sim 1/ d^{ω}$ of a diffeomorphism $f \in C^{2}$ can be $d^{θ}$ -shadowed by an exact trajectory, then $f$ is struc…

math.DS2011★ 2 cited

Lipschitz Shadowing for Flows

Kennet J. Palmer, Sergei Pilyugin, Sergey Tikhomirov

Let $ϕ$ be the flow generated by a smooth vector field $X$ on a smooth closed manifold. We show that the Lipschitz shadowing property of $ϕ$ is equivalent to the structural stabili…