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

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dc.creatorDu, Bau-Sen
dc.date2007-06-15
dc.date.accessioned2026-07-07T08:10:26Z
dc.date.available2026-07-07T08:10:26Z
dc.descriptionLet 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.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0706.2297
dc.identifierhttp://arxiv.org/abs/0706.2297
dc.identifierBull. Austral. Math. Soc. 31(1985), 89-103. Corrigendum: 32 (1985), 159
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131826
dc.subjectDynamical Systems
dc.subjectNumber Theory
dc.subject37E05 (Primary), 37C25, 37E15 (Secondary)
dc.titleThe Minimal Number of Periodic Orbits of Periods Guaranteed in Sharkovskii's Theorem
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