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Change of structure and chaos for solutions of \(\dot x\)(t) = −f(x(t−1))

  • H. Peters
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 878)

Keywords

Periodic Solution Initial Function Shift Operator Homoclinic Solution Strict Feedback 
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VI. References

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    M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J.Stat.Phys. 19, 1978, 25–52MathSciNetCrossRefzbMATHGoogle Scholar
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    T. Furumochi, Existence of periodic solutions of one-dimensional differential-delay equations, Tôhoku Math.J. 30, 1978, 13–35MathSciNetCrossRefzbMATHGoogle Scholar
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    T.Y. Li-J.A. Yorke, Period three implies chaos, Am.Math.Monthly 82, 1975, 985–992MathSciNetCrossRefzbMATHGoogle Scholar
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    R.D. Nussbaum, Periodic solutions of nonlinear autonomous functional differential equations, in "Functional Differential Equations and Approximation of Fixed Points", Springer Lecture Notes in Math. 730, 1979, 283–326Google Scholar
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    R.D. Nussbaum, Uniqueness and nonuniqueness for periodic solutions of x′(t)=−g(x(t−1)), J.Diff.Eq. 34, 1979, 25–54MathSciNetCrossRefzbMATHGoogle Scholar
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    R.D. Nussbaum-H.-O. Peitgen, Spurious and special periodic solutions of \(\dot x\)(t)=−λf(x(t−1)), to appearGoogle Scholar
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    H. Peters, Comportement chaotique d'une équation différentielle retardée, C.R.Acad.Sci. Paris 290, 1980, 1119–1122zbMATHGoogle Scholar
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    H.W. Siegberg, PhD-thesis, Bremen 1981Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • H. Peters
    • 1
  1. 1.Forschungsschwerpunkt "Dynamische Systeme" Fachbereich MathematikUniversität BremenBremen 33

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