sin(1/x)连续统上每个点都为链回归点的映射
Maps of the sin(1/x) Continuum with Every Point Chain Recurrent
摘要:
设S为sin(1/x)连续统,f:S→S为连续自映射,其中S=L1∪L2 ,L1={(x,y)∈R2|x=0,-1≤y≤1} ,L2={(x,y)∈R2|sin(1/x),0≤x≤1} 。本文指出:如果f为逐点链回归映射,那么,若Fin(f) 连通,则f为恒等映射;若Fin(f) 不连通,则当Fin(f1) 或者Fin(f2) 非退化不连通时, f含湍流,当Fin(f1)=L1 , Fin(f2)=a,a∈L2且(L2-{a})∩P(f2)=φ 时, f不含湍流。
Abstract:
Let S be sin(1/x) continuum and f:S→S is a continuous map, where S=L1∪L2 , L1={(x,y)∈R2|x=0,-1≤y≤1} , L2={(x,y)∈R2|sin(1/x),0≤x≤1} . It is showed that if f is pointwise chain recurrent, then if Fin(f) is connected, f is identify; if Fin(f) is disconnected, then f is turbulent while Fin(f1) or Fin(f2) is nondegenerate disconnected; f is not turbulent while Fin(f1)=L1 , Fin(f2)=a,a∈L2 and (L2-{a})∩P(f2)=φ.
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