TY - JOUR

T1 - Sets of dynamical systems with various limit shadowing properties

AU - Pilyugin, Sergei Yu

N1 - Funding Information: This research was supported by the Russian Foundation for Basic Research (project 05-01-01079). The author is grateful to K. Sakai for valuable advices and to the anonymous referee whose comments helped to improve the presentation.

PY - 2007/9

Y1 - 2007/9

N2 - We study the C 1-interiors of sets of diffeomorphisms of a closed smooth manifold with various limit shadowing properties. It is shown that, for some natural analogs of the usual limit shadowing property, the corresponding C 1-interiors coincide with the set of Ω-stable diffeomorphisms. The same problem is considered for two-sided analogs of the limit shadowing property.

AB - We study the C 1-interiors of sets of diffeomorphisms of a closed smooth manifold with various limit shadowing properties. It is shown that, for some natural analogs of the usual limit shadowing property, the corresponding C 1-interiors coincide with the set of Ω-stable diffeomorphisms. The same problem is considered for two-sided analogs of the limit shadowing property.

KW - Hyperbolicity

KW - Limit shadowing

KW - Structural stability

KW - Transversality

UR - http://www.scopus.com/inward/record.url?scp=35348934401&partnerID=8YFLogxK

U2 - 10.1007/s10884-007-9073-2

DO - 10.1007/s10884-007-9073-2

M3 - Article

AN - SCOPUS:35348934401

VL - 19

SP - 747

EP - 775

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 3

ER -