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)


Periodic Solution Initial Function Shift Operator Homoclinic Solution Strict Feedback 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

VI. References

  1. [1]
    M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J.Stat.Phys. 19, 1978, 25–52MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    T. Furumochi, Existence of periodic solutions of one-dimensional differential-delay equations, Tôhoku Math.J. 30, 1978, 13–35MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    T.Y. Li-J.A. Yorke, Period three implies chaos, Am.Math.Monthly 82, 1975, 985–992MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    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
  5. [5]
    R.D. Nussbaum, Uniqueness and nonuniqueness for periodic solutions of x′(t)=−g(x(t−1)), J.Diff.Eq. 34, 1979, 25–54MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    R.D. Nussbaum-H.-O. Peitgen, Spurious and special periodic solutions of \(\dot x\)(t)=−λf(x(t−1)), to appearGoogle Scholar
  7. [7]
    H. Peters, Comportement chaotique d'une équation différentielle retardée, C.R.Acad.Sci. Paris 290, 1980, 1119–1122zbMATHGoogle Scholar
  8. [8]
    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

Personalised recommendations