Standard

Transversality properties and C1-open sets of diffeomorphisms with weak shadowing. / Pilyugin, S. Yu; Sakai, K.; Tarakanov, O. A.

In: Discrete and Continuous Dynamical Systems, Vol. 16, No. 4, 12.2006, p. 871-882.

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

Harvard

Pilyugin, SY, Sakai, K & Tarakanov, OA 2006, 'Transversality properties and C1-open sets of diffeomorphisms with weak shadowing', Discrete and Continuous Dynamical Systems, vol. 16, no. 4, pp. 871-882.

APA

Pilyugin, S. Y., Sakai, K., & Tarakanov, O. A. (2006). Transversality properties and C1-open sets of diffeomorphisms with weak shadowing. Discrete and Continuous Dynamical Systems, 16(4), 871-882.

Vancouver

Pilyugin SY, Sakai K, Tarakanov OA. Transversality properties and C1-open sets of diffeomorphisms with weak shadowing. Discrete and Continuous Dynamical Systems. 2006 Dec;16(4):871-882.

Author

Pilyugin, S. Yu ; Sakai, K. ; Tarakanov, O. A. / Transversality properties and C1-open sets of diffeomorphisms with weak shadowing. In: Discrete and Continuous Dynamical Systems. 2006 ; Vol. 16, No. 4. pp. 871-882.

BibTeX

@article{8e52baa526ba48119eb1605fbeb899e9,
title = "Transversality properties and C1-open sets of diffeomorphisms with weak shadowing",
abstract = "Let Int1 WS(M) be the C1-interior of the set of diffeomorphisms of a smooth closed manifold M having the weak shadowing property. The second author has shown that if dim M = 2 and all of the sources and sinks of a diffeomorphism f ∈ Int1WS(M) are trivial, then f is structurally stable. In this paper, we show that there exist diffeomorphisms f ∈ Int1WS(M), dim M = 2, such that (i) f belongs to the C 1-interior of diffeomorphisms for which the C0- transversality condition is not satisfied, (ii) f has a saddle connection. These results are based on the following theorem: if the phase diagram of an Ω-stable diffeomorphism f of a manifold M of arbitrary dimension does not contain chains of length m > 3, then f has the weak shadowing property.",
keywords = "Axiom A, No-cycle condition, Shadowing property, Transversality condition, Weak shadowing property",
author = "Pilyugin, {S. Yu} and K. Sakai and Tarakanov, {O. A.}",
year = "2006",
month = dec,
language = "English",
volume = "16",
pages = "871--882",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "4",

}

RIS

TY - JOUR

T1 - Transversality properties and C1-open sets of diffeomorphisms with weak shadowing

AU - Pilyugin, S. Yu

AU - Sakai, K.

AU - Tarakanov, O. A.

PY - 2006/12

Y1 - 2006/12

N2 - Let Int1 WS(M) be the C1-interior of the set of diffeomorphisms of a smooth closed manifold M having the weak shadowing property. The second author has shown that if dim M = 2 and all of the sources and sinks of a diffeomorphism f ∈ Int1WS(M) are trivial, then f is structurally stable. In this paper, we show that there exist diffeomorphisms f ∈ Int1WS(M), dim M = 2, such that (i) f belongs to the C 1-interior of diffeomorphisms for which the C0- transversality condition is not satisfied, (ii) f has a saddle connection. These results are based on the following theorem: if the phase diagram of an Ω-stable diffeomorphism f of a manifold M of arbitrary dimension does not contain chains of length m > 3, then f has the weak shadowing property.

AB - Let Int1 WS(M) be the C1-interior of the set of diffeomorphisms of a smooth closed manifold M having the weak shadowing property. The second author has shown that if dim M = 2 and all of the sources and sinks of a diffeomorphism f ∈ Int1WS(M) are trivial, then f is structurally stable. In this paper, we show that there exist diffeomorphisms f ∈ Int1WS(M), dim M = 2, such that (i) f belongs to the C 1-interior of diffeomorphisms for which the C0- transversality condition is not satisfied, (ii) f has a saddle connection. These results are based on the following theorem: if the phase diagram of an Ω-stable diffeomorphism f of a manifold M of arbitrary dimension does not contain chains of length m > 3, then f has the weak shadowing property.

KW - Axiom A

KW - No-cycle condition

KW - Shadowing property

KW - Transversality condition

KW - Weak shadowing property

UR - http://www.scopus.com/inward/record.url?scp=33846128809&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33846128809

VL - 16

SP - 871

EP - 882

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 4

ER -

ID: 92248323