INVERSE SHADOWING PROPERTY OF MORSE-SMALE SYSTEMS

  • Choi, Taeyoung (Department of Mathematics Chungnam National University) ;
  • Lee, Keonhee (Department of Mathematics Chungnam National University)
  • Received : 2002.05.16
  • Published : 2002.08.01

Abstract

We consider the inverse shadowing property of a dynamical system which is an "inverse" form of the shadowing property of the system. In particular, we show that every Morse-Smale system f on a compact smooth manifold has the inverse shadowing property with respect to the class $\mathcal{T}_h(f)$ of continuous methods generated by homeomorphisms, but the system f does not have the inverse\mathrm{T} shadowing property with respect to the class $\mathcal{T}_c(f)$ of continuous methods.

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