Positive sequence topological entropy characterizes chaotic maps

Franzová, N.; Smítal, J.

doi:10.1090/S0002-9939-1991-1062387-3

Positive sequence topological entropy characterizes chaotic maps
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by N. Franzová and J. Smítal PDF

Proc. Amer. Math. Soc. 112 (1991), 1083-1086 Request permission

Abstract:

We prove that a continuous map $f$ of the interval is chaotic (in the sense of Li and Yorke) iff its sequence topological entropy ${h_A}(f)$ relative to a suitable increasing sequence $A$ of times is positive. This result is interesting since the ordinary topological entropy $h(f)$ of chaotic maps can be zero.

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