回归点集为闭集的线段连续自映射的周期点的周期(英文)

Let I be an interval (i. e., a connected subset of the real line), and f:I→J be continouos. The sets of periodic points, recurrent points and nonwandering points of f are denoted by p(f), R(f) and Ω(f) respectively. In 1], 2] and 3] i has been proved that if the set P(f) is closed, then the period of each periodic point of f is a power of 2. This result is improved by the following theorem.