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  • Inverse shadowing and related measures

    Publication

    - Science China-Mathematics - Year 2020

    We study various weaker forms of the inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called ergodic inverse shadowing property (Birkhoff averages of continuous functions along an exact trajectory and the approximating one are close). We demonstrate that this property implies the continuity of the set of invariant measures in the Hausdorff metric. We show that the...

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  • Partial hyperbolicity and central shadowing

    Publication

    We study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.

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  • Partial hyperbolicity and central shadowing

    Publication

    - Discrete & Continuous Dynamical Systems - A - Year 2013

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  • Weak forms of shadowing in topological dynamics

    Publication

    We consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...

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  • Shadowing is generic---a continuous map case

    Publication

    - Discrete & Continuous Dynamical Systems - A - Year 2014

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