逆极限空间上的ε-紊动

ε-Chaos on Inverse Limit Space

中文关键词:  逆极限空间  移位映射  ε-紊动．

英文关键词:inverse limit space  shift map  ε-chaos.

中文摘要:

      设ｆ是紧致度量空间上的满映射，σ_ｆ为ｆ的逆极限空间上的移位映射．本文证明，存在ε，ε′＞０，ｆ是ε-紊动的当且仅当σ_ｆ是ε′-紊动的．此外，本文还讨论了ｆ是非满映射和线段自映射的情形．

英文摘要:

      Let f be a surjective to map of a compact metric space and denote by σ_ｆ the shift map of the inverse limit space. We prove that there exist ε and ε′>0 , f is ε-chaos iff σ_ｆ is ε′-chaos; On the other hand, we also consider the condition as f is not onto or f is interval map.