Far East Journal of Dynamical Systems
Volume 4, Issue 1, Pages 1 - 15
(June 2002)
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TOPOLOGICAL ENTROPY AND PSEUDO-ENTROPY
Sung Kyu Choi (Korea), Chin-Ku Chu (Korea) and Jong Suh Park (Korea)
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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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