ε-Chaos on Inverse Limit Space

Abstract:

      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.