On Topological Sequence Entropy and Chaotic Maps on Inverse Limit Spaces
نویسندگان
چکیده
The aim of this paper is to prove the following results: a continuous map f : [0, 1]→ [0, 1] is chaotic iff the shift map σf : lim ← ([0, 1], f)→ lim ← ([0, 1], f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. σf : lim ← ([0, 1], f) → lim ← ([0, 1], f) is chaotic iff there exists an increasing sequence of positive integers A such that the topological sequence entropy hA(σf ) > 0. Finally, for any A there exists a chaotic continuous map fA : [0, 1] → [0, 1] such that hA(σfA ) = 0.
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