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## Fundamenta Mathematicae

### Tom 168 / 2001

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

#### Streszczenie

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.

#### Autorzy

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

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