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ON THE NUMBER OF PERIODIC ORBITS OF CONTINUOUS MAPPINGS OF THE INTERVAL

Jaume Llibre and Agustí Reventós
Publicacions de la Secció de Matemàtiques
No. 25 (JUNY 1981), pp. 97-106
Stable URL: http://www.jstor.org/stable/43741888
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
ON THE NUMBER OF PERIODIC ORBITS OF CONTINUOUS MAPPINGS OF THE INTERVAL
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Abstract

Let f be a continuous map of a closed interval into itself, and let P(f) denote the set of positive integers k such that f has a periodic point of period k. Consider the following ordering of positive integers: 3,5,7,...,2.3,2.5,2.7,...,4.3,4.5,4.7,...,8,4,2,1. Sarkovskii's theorem states that if n ∊ P(f) and m is to the right of n in the above ordering then m ∊ P(f). We may ask the following question: if n ∊ P(f) and m is to the right of n in the above ordering what can be said about the number of periodic orbits of f of period m ?. We give the answer to this question if n is either odd or a power of 2.

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