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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 language | English |
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Pages (from-to) | 871-882 |
Number of pages | 12 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 16 |
Issue number | 4 |
State | Published - Dec 2006 |
ID: 92248323