Geodesic
Diffeomorphisms with weak shadowing
Kazuhiro Sakai1
1 Department of Mathematics Kanagawa University Yokohama 221-8686, Japan
Fundamenta Mathematicae, Tome 168 (2001) no. 1, pp. 57-75

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm168-1-2
Keywords: weak shadowing property really weaker shadowing property proved every element interior set diffeomorphisms infty closed surface having weak shadowing property satisfies axiom no cycle condition result does generalize higher dimensions non wandering set diffeomorphism belonging interior finite only morse smale

Kazuhiro Sakai 1

1 Department of Mathematics Kanagawa University Yokohama 221-8686, Japan 
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Kazuhiro Sakai. Diffeomorphisms with weak shadowing. Fundamenta Mathematicae, Tome 168 (2001) no. 1, pp. 57-75. doi: 10.4064/fm168-1-2

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