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

DOI10.1017/S0004972700002306zbMath0582.54027arXiv0706.2297OpenAlexW2962955796MaRDI QIDQ3704605

Bau-Sen Du

Publication date: 1985

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.2297

zbMATH Keywords

piecewise linear mapsSharkovskij orderinglower bound on the number of periodic orbitsmaps on a compact real intervalperiodic orbit of minimal period

Mathematics Subject Classification ID

Related Items (4)

Positive subharmonic solutions to superlinear ODEs with indefinite weight ⋮ Topological entropy and chaos of interval maps ⋮ Sharkovskii's ordering and estimates of the number of periodic trajectories of given period of a self-map of an interval ⋮ Congruence identities arising from dynamical systems

Cites Work

• Unnamed Item
• A graph-theoretic proof of Sharkovsky's theorem on the periodic points of continuous functions
• Interval mapping graphs and periodic points of continuous functions
• Structure of mappings of an interval with zero entropy
• The periodic points of maps of the disk and the interval
• A theorem of Sarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line
• Periodic Orbits and Kneading Invariants
• Period Three Implies Chaos

This page was built for publication: The minimal number of periodic orbits of periods guaranteed in Sharkovskii's theorem