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C1 interiors of sets of systems with various shadowing properties. / Pilyugin, Sergei Yu; Sakai, Kazuhiro.

Lecture Notes in Mathematics. Springer Nature, 2017. стр. 125-179 (Lecture Notes in Mathematics; Том 2193).

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Harvard

Pilyugin, SY & Sakai, K 2017, C1 interiors of sets of systems with various shadowing properties. в Lecture Notes in Mathematics. Lecture Notes in Mathematics, Том. 2193, Springer Nature, стр. 125-179. https://doi.org/10.1007/978-3-319-65184-2_3

APA

Pilyugin, S. Y., & Sakai, K. (2017). C1 interiors of sets of systems with various shadowing properties. в Lecture Notes in Mathematics (стр. 125-179). (Lecture Notes in Mathematics; Том 2193). Springer Nature. https://doi.org/10.1007/978-3-319-65184-2_3

Vancouver

Pilyugin SY, Sakai K. C1 interiors of sets of systems with various shadowing properties. в Lecture Notes in Mathematics. Springer Nature. 2017. стр. 125-179. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-319-65184-2_3

Author

Pilyugin, Sergei Yu ; Sakai, Kazuhiro. / C1 interiors of sets of systems with various shadowing properties. Lecture Notes in Mathematics. Springer Nature, 2017. стр. 125-179 (Lecture Notes in Mathematics).

BibTeX

@inbook{8169c961714743cfaaedc8ab49cd3e07,
title = "C1 interiors of sets of systems with various shadowing properties",
abstract = "In this chapter, we study the structure of C1 interiors of some basic sets of dynamical systems having various shadowing properties. We give either complete proofs or schemes of proof of the following main results: • The C1 interior of the set of diffeomorphisms having the standard shadowing property is a subset of the set of structurally stable diffeomorphisms (Theorem 3.1.1); this result and Theorem 1.4.1 (a) imply that the C1 interior of the set of diffeomorphisms having the standard shadowing property coincides with the set of structurally stable diffeomorphisms; • the set Int1.OrientSPF n B/ is a subset of the set of structurally stable vector fields (Theorem 3.3.1); similarly to the case of diffeomorphisms, this result and Theorem 1.4.1 (b) imply that the set Int1.OrientSPF n B/ coincides with the set of structurally stable vector fields; • the set Int1.OrientSPF/ contains vector fields that are not structurally stable (Theorem 3.4.1).",
author = "Pilyugin, {Sergei Yu} and Kazuhiro Sakai",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "2017",
doi = "10.1007/978-3-319-65184-2_3",
language = "English",
series = "Lecture Notes in Mathematics",
publisher = "Springer Nature",
pages = "125--179",
booktitle = "Lecture Notes in Mathematics",
address = "Germany",

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RIS

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T1 - C1 interiors of sets of systems with various shadowing properties

AU - Pilyugin, Sergei Yu

AU - Sakai, Kazuhiro

N1 - Publisher Copyright: © Springer International Publishing AG 2017. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

N2 - In this chapter, we study the structure of C1 interiors of some basic sets of dynamical systems having various shadowing properties. We give either complete proofs or schemes of proof of the following main results: • The C1 interior of the set of diffeomorphisms having the standard shadowing property is a subset of the set of structurally stable diffeomorphisms (Theorem 3.1.1); this result and Theorem 1.4.1 (a) imply that the C1 interior of the set of diffeomorphisms having the standard shadowing property coincides with the set of structurally stable diffeomorphisms; • the set Int1.OrientSPF n B/ is a subset of the set of structurally stable vector fields (Theorem 3.3.1); similarly to the case of diffeomorphisms, this result and Theorem 1.4.1 (b) imply that the set Int1.OrientSPF n B/ coincides with the set of structurally stable vector fields; • the set Int1.OrientSPF/ contains vector fields that are not structurally stable (Theorem 3.4.1).

AB - In this chapter, we study the structure of C1 interiors of some basic sets of dynamical systems having various shadowing properties. We give either complete proofs or schemes of proof of the following main results: • The C1 interior of the set of diffeomorphisms having the standard shadowing property is a subset of the set of structurally stable diffeomorphisms (Theorem 3.1.1); this result and Theorem 1.4.1 (a) imply that the C1 interior of the set of diffeomorphisms having the standard shadowing property coincides with the set of structurally stable diffeomorphisms; • the set Int1.OrientSPF n B/ is a subset of the set of structurally stable vector fields (Theorem 3.3.1); similarly to the case of diffeomorphisms, this result and Theorem 1.4.1 (b) imply that the set Int1.OrientSPF n B/ coincides with the set of structurally stable vector fields; • the set Int1.OrientSPF/ contains vector fields that are not structurally stable (Theorem 3.4.1).

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T3 - Lecture Notes in Mathematics

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