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arXiv · 0706.2297

The Minimal Number of Periodic Orbits of Periods Guaranteed in Sharkovskii's Theorem

Bau-Sen Du
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Abstract

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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Bau-Sen Du. 2007-06-15. The Minimal Number of Periodic Orbits of Periods Guaranteed in Sharkovskii's Theorem. https://arxiv.org/abs/0706.2297

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