Sets of Recurrent Points of Continuous Maps of the Interval

摘要

For a continuous map of the interval the following conditions are equivalent: (1) the period of every periodic point is a power of 2, (2) R-bar sup((+)) intersection R-bar sup((-))-R=phi and (3) R-bar-R is countable, where R denotes the set of recurrent points, R-bar is the closure of R, and R-barsup((+)) (or R-barsup((-))) is the right-side closure (left-side closure, respectively) of R. (Atomindex citation 16:018797)