关于圆周自映射的一个注记(英文)

A note on continuous circle maps

设S1 是一个圆周 ,f:S1 →S1 是连续映射 .我们证明以下结论不仅对含有周期点的圆周映射成立 ,也对一般的圆周映射f成立 ,这个结论是R(f) Λ(R(f) ) Λ(Λ(f) ) Λ(Ω(f) ) (R(f) ) Λ(f) Ω(f) .

Let S 1 be a circle and f:S 1→S 1 be a continuous map.In this note,we mainly prove that the following conclusion is true not only for a circte map with a periodic point but also for a general circle map f.It is R(f) Λ(R(f) ) Λ(Λ(f)) Λ(Ω(f)) R(f) ) Λ(f) Ω(f) .Here we use some properties on a gragh map.