The chain recurrent set for maps of the interval

Louis Block, John E. Franke
1983 Proceedings of the American Mathematical Society  
Let/be a continuous map of a compact interval into itself. We show that if the set of periodic points of/ is a closed set then every chain recurrent point is periodic
doi:10.1090/s0002-9939-1983-0687650-2 fatcat:ioabbkq745bchh3egfwt63n534