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