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Main Definitions and Basic Results

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Shadowing and Hyperbolicity

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2193))

Abstract

In this preliminary chapter, we define pseudotrajectories and various shadowing properties for dynamical systems with discrete and continuous time (Sects. 1.1 and 1.2), study the notion of chain transitivity (Sect. 1.1), describe hyperbolicity, Ω-stability, and structural stability (Sect. 1.3), and prove a lemma on finite Lipschitz shadowing in a neighborhood of a hyperbolic set (Sect. 1.4).

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    Sergei Yu. Pilyugin

  2. Faculty of Education, Utsunomiya University, Utsunomiya, Japan

    Kazuhiro Sakai

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  1. Sergei Yu. Pilyugin
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  2. Kazuhiro Sakai
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Pilyugin, S.Y., Sakai, K. (2017). Main Definitions and Basic Results. In: Shadowing and Hyperbolicity. Lecture Notes in Mathematics, vol 2193. Springer, Cham. https://doi.org/10.1007/978-3-319-65184-2_1

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