Sergey Tikhomirov

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We prove that for any closed manifold of dimension 3 or greater there is an open set of smooth flows that have a hyper-bolic set that is not contained in a locally maximal one. Additionally , we show that the stabilization of the shadowing closure of a hyperbolic set is an intrinsic property for premaximality. Lastly, we review some results due to Anosov(More)
For any θ, ω > 1/2 we prove that, if any d-pseudotrajectory of length ∼ 1/d ω of a diffeomorphism f ∈ C 2 can be d θ-shadowed by an exact trajectory, then f is structurally stable. Previously it was conjectured [9, 10] that for θ = ω = 1/2 this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof we introduce the notion(More)
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