WEAK INVERSE SHADOWING AND Ω-STABILITY

  • Zhang, Yong (Department of Mathematics Suzhou University) ;
  • Choi, Taeyoung (Department of Mathematics Chungnam National University)
  • Received : 2004.06.16
  • Published : 2004.10.31

Abstract

We give characterization of ${\Omega}$-stable diffeomorphisms via the notions of weak inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of diffeomorphisms with the weak inverse shadowing property with respect to the class $\mathcal{T}_h$ coincides with the set of ${\Omega}$-stable diffeomorphisms.

Keywords