廖公夫.周期点集为闭集的圆周自映射周期点的周期[J].数学研究及应用,1985,5(3):15~16
周期点集为闭集的圆周自映射周期点的周期
Periods of Periodic Points of Maps of the Circle whose Periodic Points form a Closed Set
投稿时间:1982-10-11  
DOI:10.3770/j.issn:1000-341X.1985.03.005
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廖公夫 吉林大学数学系 
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英文摘要:
      Let S1 denote the circle. In this paper, we show the following.Theorem. Let f: S1→S1 be a continuous map and suppose f has a fixed point and the set of periodic points of f is closed, then the period of each periodic point of f is a power of 2.Corollary. Let f: S1→S1 be a continuous map and suppose the set of periodic points of f is closed, then there exists an odd integer m such that the set of periods of periodic points of f is contained in the set {m·2n; n = 0,1,2,…}.
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