Lipschitz and hölder shadowing and structural stability

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Lipschitz and hölder shadowing and structural stability. / Pilyugin, Sergei Yu; Sakai, Kazuhiro.

In: Lecture Notes in Mathematics, Vol. 2193, 2017, p. 37-124.

Research output: Contribution to journal › Article › peer-review

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Pilyugin, Sergei Yu ; Sakai, Kazuhiro. / Lipschitz and hölder shadowing and structural stability. In: Lecture Notes in Mathematics. 2017 ; Vol. 2193. pp. 37-124.

BibTeX

@article{ef65912fae72463ba0b67a5d937dc9b6,

title = "Lipschitz and h{\"o}lder shadowing and structural stability",

abstract = "In this chapter, we give either complete proofs or schemes of proof of the following main results: • If a diffeomorphism f of a smooth closed manifold has the Lipschitz shadowing property, then f is structurally stable (Theorem 2.3.1); • a diffeomorphism f has the Lipschitz periodic shadowing property if and only if f is Ω-stable (Theorem 2.4.1); • if a diffeomorphism f of class C2 has the H{\"o}lder shadowing property on finite intervals with constants L;C; d0; θ; ω, where θ ϵ (.1/2, 1) and θ+ω > 1, then f is structurally stable (Theorem 2.5.1); • there exists a homeomorphism of the interval that has the Lipschitz shadowing property and a nonisolated fixed point (Theorem 2.6.1); • if a vector field X has the Lipschitz shadowing property, then X is structurally stable (Theorem 2.7.1).",

author = "Pilyugin, {Sergei Yu} and Kazuhiro Sakai",

year = "2017",

doi = "10.1007/978-3-319-65184-2_2",

language = "English",

volume = "2193",

pages = "37--124",

journal = "Lecture Notes in Mathematics",

issn = "0075-8434",

publisher = "Springer Nature",

}

RIS

TY - JOUR

T1 - Lipschitz and hölder shadowing and structural stability

AU - Pilyugin, Sergei Yu

AU - Sakai, Kazuhiro

PY - 2017

Y1 - 2017

N2 - In this chapter, we give either complete proofs or schemes of proof of the following main results: • If a diffeomorphism f of a smooth closed manifold has the Lipschitz shadowing property, then f is structurally stable (Theorem 2.3.1); • a diffeomorphism f has the Lipschitz periodic shadowing property if and only if f is Ω-stable (Theorem 2.4.1); • if a diffeomorphism f of class C2 has the Hölder shadowing property on finite intervals with constants L;C; d0; θ; ω, where θ ϵ (.1/2, 1) and θ+ω > 1, then f is structurally stable (Theorem 2.5.1); • there exists a homeomorphism of the interval that has the Lipschitz shadowing property and a nonisolated fixed point (Theorem 2.6.1); • if a vector field X has the Lipschitz shadowing property, then X is structurally stable (Theorem 2.7.1).

AB - In this chapter, we give either complete proofs or schemes of proof of the following main results: • If a diffeomorphism f of a smooth closed manifold has the Lipschitz shadowing property, then f is structurally stable (Theorem 2.3.1); • a diffeomorphism f has the Lipschitz periodic shadowing property if and only if f is Ω-stable (Theorem 2.4.1); • if a diffeomorphism f of class C2 has the Hölder shadowing property on finite intervals with constants L;C; d0; θ; ω, where θ ϵ (.1/2, 1) and θ+ω > 1, then f is structurally stable (Theorem 2.5.1); • there exists a homeomorphism of the interval that has the Lipschitz shadowing property and a nonisolated fixed point (Theorem 2.6.1); • if a vector field X has the Lipschitz shadowing property, then X is structurally stable (Theorem 2.7.1).

UR - http://www.scopus.com/inward/record.url?scp=85029102480&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-65184-2_2

DO - 10.1007/978-3-319-65184-2_2

M3 - Article

AN - SCOPUS:85029102480

VL - 2193

SP - 37

EP - 124

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

SN - 0075-8434

ER -

ID: 74985680