Diffeomorphisms with weak shadowing

Volume 168 / 2001

Kazuhiro Sakai Fundamenta Mathematicae 168 (2001), 57-75 MSC: 37B99, 37C50, 37C75, 37D15, 37D20. DOI: 10.4064/fm168-1-2


The weak shadowing property is really weaker than the shadowing property. It is proved that every element of the $C^1$ interior of the set of all diffeomorphisms on a $C^\infty $ closed surface having the weak shadowing property satisfies Axiom A and the no-cycle condition (this result does not generalize to higher dimensions), and that the non-wandering set of a diffeomorphism $f$ belonging to the $C^1$ interior is finite if and only if $f$ is Morse–Smale.


  • Kazuhiro SakaiDepartment of Mathematics
    Kanagawa University
    Yokohama 221-8686, Japan

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