aequationes mathematicae

, Volume 45, Issue 2–3, pp 195–206 | Cite as

Sur les solutions globales de l'équation des cocycles

  • Mohamed Hmissi
Research Papers

Summary

Let Ф:ℝ+ ×X ↦ X be a semidynamical system andf:ℝ+ × X ↦ ℝ+ be a cocycle of (X, Ф), i.e.,f satisfies the following functional equation:
$$\forall x \in X;s,t \geqslant 0:f(s + t,x) = f(t,x)f(s,\Phi (t,x)).$$
(E)

Under convenient conditions we give an explicit form of the globally measurable or continuous solutions of (E) and we study the particular case whenX = ℝ.

AMS (1991) subject classification

39B 58F 

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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • Mohamed Hmissi
    • 1
  1. 1.Département de MathématiquesFaculté des Sciences de TunisBelvédèreTunisia

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