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SOME PROPERTIES OF THE STRONG CHAIN RECURRENT SET

  • Fakhari, Abbas (Department of Mathematics and Computer Sciences, Damghan University of Basic Science) ;
  • Ghane, Fatomeh Helen (Department of Mathematics, Ferdowsi University) ;
  • Sarizadeh, Aliasghar (Department of Mathematics, Islamic Azad University)
  • Published : 2010.01.31

Abstract

The article is devoted to exhibit some general properties of strong chain recurrent set and strong chain transitive components for a continuous map f on a compact metric space X. We investigate the relation between the weak shadowing property and strong chain transitivity. It is shown that a continuous map f from a compact metric space X onto itself with the average shadowing property is strong chain transitive.

Keywords

chain recurrent;strong-chain recurrent;strong-chain recurrent class;weak shadowing;average shadowing

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