Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Lipschitz and hölder shadowing and structural stability. / Pilyugin, Sergei Yu; Sakai, Kazuhiro.
в: Lecture Notes in Mathematics, Том 2193, 2017, стр. 37-124.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Lipschitz and hölder shadowing and structural stability
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 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