Mathematics – Dynamical Systems
Scientific paper
2007-06-15
Bull. Austral. Math. Soc. 31(1985), 89-103. Corrigendum: 32 (1985), 159
Mathematics
Dynamical Systems
11 pages
Scientific paper
Let f(x) be a continuous function from a compact real interval into itself with a periodic orbit of minimal period m, where m is not an integral power of 2. Then, by Sharkovsky's theorem, for every positive integer n with m \prec n in the Sharkovsky's ordering defined below, a lower bound on the number of periodic orbits of f(x) with minimal period n is 1. Could we improve this lower bound from 1 to some larger number? In this paper, we give a complete answer to this question.
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