Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-27T12:47:12.359Z Has data issue: false hasContentIssue false

On Sharkovsky's cycle coexistence ordering

Published online by Cambridge University Press:  17 April 2009

Peter E. Kloeden
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, Western Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A theorem of Sharkovsky on the coexistence of cycles for one-dimensional difference equations is generalized to a class of difference equations of arbitary dimension. The mappings defining these difference equations are such that the ith component depends only on the first i independent variables.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Guckenheimer, J., Oster, G. and Ipaktchi, A., “The dynamics of density dependent population models”, J. Math. Biol. 4 (1977), 101147.Google Scholar
[2]Kloeden, Peter, Deakin, Michael A.B., Tirkel, A.Z., “A precise definition of chaos”, Nature 264 (1976), 295.CrossRefGoogle Scholar
[3]Li, Tien-Yien and Yorke, James A., “Period three implies chaos”, Amer. Math. Monthly 82 (1975), 985992.CrossRefGoogle Scholar
[4]ШаРκоВсκиЙ, A.H. [Sharkovsky, A.N.], “СосЩествование цинлов непрерывного преобразования прямоЙ в себя” [Co-existence of the cycles of a continuous mapping of the line into itself], Ukrain. Mat. Ž 16 (1964), 6171.Google Scholar
[5]Štefan, P., “A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line”, Commun. Math. Phys. 54 (1977), 237248.CrossRefGoogle Scholar