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The minimal number of periodic orbits of periods guaranteed in Sharkovskii's theorem

Published online by Cambridge University Press:  17 April 2009

Bau-Sen Du
Bau-Sen Du
Affiliation:
Institute of Mathematics, Acadmia Sinica, Nankang, Taipei, Taiwan 115, Republic of China.
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Abstract

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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 Sharkovskii's theorem, for every positive integer n with m → n in the Sharkovskii 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 1 , February 1985 , pp. 89 - 103
Copyright
Copyright © Australian Mathematical Society 1985

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