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.

Original languageEnglish
Pages (from-to)871-882
Number of pages12
JournalDiscrete and Continuous Dynamical Systems
Volume16
Issue number4
StatePublished - Dec 2006

    Research areas

  • Axiom A, No-cycle condition, Shadowing property, Transversality condition, Weak shadowing property

    Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

ID: 92248323