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Volume 4, Issue 2
Pg 81 - 156 (December 2002)

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Far East Journal of Dynamical Systems

Far East Journal of Dynamical Systems
Volume 4, Issue 1, Pages 1 - 15 (June 2002)

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.

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