Diffeomorphisms with weak shadowing (Q2717684)

The author studies the property of weak shadowing in dynamical systems introduced by \textit{R. M. Corless} and the reviewer [J. Math. Anal. Appl. 189, 409-423 (1995; Zbl 0821.58036)]. He investigates the \(C^1\)-interior \(I\) of the set of diffeomorphisms of a \(C^{\infty}\) closed surface having the weak shadowing property. NEWLINENEWLINENEWLINEIt is shown that any system in \(I\) satisfies Axiom A and the no-cycle condition (due to the existence of \(C^1\)-open sets of topologically transitive non-Anosov diffeomorphisms on the three-torus, this result cannot be generalized to dimensions \(n>2\)). In addition, the nonwandering set of a diffeomorphism \(f\in I\) is finite if and only if \(f\) is a Morse-Smale diffeomorphism.