Stability of chain recurrent points of continuous maps on interval

Abstract

Recently, J. Smítal and T.H. Steele [J. Difference Equ. Appl. 15 (2009), 77–86] considered the mappings C and NW, which take a function to its centre , and to its set of non-wandering points , respectively. They characterize a function at which maps C and NW are continuous, and put a problem whether the same characterization is true for the map CR, which takes an to its set of chain recurrent points . We show that the answer is positive.