TOPOLOGICAL ENTROPY AND PSEUDO-ENTROPY

Sung Kyu Choi (Korea), Chin-Ku Chu (Korea) and Jong Suh Park (Korea)

Abstract

We show that two topological entropies defined by open covers in [Trans. Amer. Math. Soc. 114 (1965), 309-319] and by (n, e)-separated sets in [Trans. Amer. Math. Soc. 153 (1971), 401-414], respectively, are the same for a compact metric space. Moreover, we prove that pseudo-entropy is equal to the topological entropy for a compact metric space. The proofs depend on easier methods than those in [Lecture Notes in Math. 458, Springer-Verlag, Berlin, 1975] and [Proc. Amer. Math. Soc. 109 (1990), 559-566], respectively.

Keywords and phrases: topological entropy, pseudo-entropy.