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.

Язык оригиналаанглийский
Страницы (с-по)871-882
Число страниц12
ЖурналDiscrete and Continuous Dynamical Systems
Том16
Номер выпуска4
СостояниеОпубликовано - дек 2006

    Предметные области Scopus

  • Анализ
  • Дискретная математика и комбинаторика
  • Прикладная математика

ID: 92248323