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On Sharkovsky's cycle coexistence ordering

  • Peter E. Kloeden (a1)
Abstract

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.

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[1]J. Guckenheimer , G. Oster and A. Ipaktchi , “The dynamics of density dependent population models”, J. Math. Biol. 4 (1977), 101147.

[2]Peter Kloeden , Michael A.B. Deakin , A.Z. Tirkel , “A precise definition of chaos”, Nature 264 (1976), 295.

[3]Tien-Yien Li and James A. Yorke , “Period three implies chaos”, Amer. Math. Monthly 82 (1975), 985992.

[5]P. Štefan , “A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line”, Commun. Math. Phys. 54 (1977), 237248.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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