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Commun. Korean Math. Soc. 2010; 25(1): 97-104
Printed March 1, 2010
https://doi.org/10.4134/CKMS.2010.25.1.97
Copyright © The Korean Mathematical Society.
Some properties of the strong chain recurrent set
Abbas Fakhari, Fatomeh Helen Ghane, and Aliasghar Sarizadeh
Damghan University of Basic Science, Ferdowsi University, and Islamic Azad University
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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