Some properties of the strong chain recurrent set
Commun. Korean Math. Soc. 2010 Vol. 25, No. 1, 97-104
https://doi.org/10.4134/CKMS.2010.25.1.97
Printed March 1, 2010
Abbas Fakhari, Fatomeh Helen Ghane, and Aliasghar Sarizadeh
Damghan University of Basic Science, Ferdowsi University, and Islamic Azad University
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
MSC numbers : Primary 54H20, 37B40, Secondary 58F99
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