  We build bounded solutions to a linear integral equation. Our functions are
built as limit of iterated Birkhoff sums over auto-similar dynamical systems.
  Nous construisons des solutions born\'ees \`a une \'equation int\'egrale.
Notre m\'ethode repose sur une limite de sommes de Birkhoff it\'er\'ees
au-dessus de certains syst\`emes dynamiques auto-similaires.

Dynamical Systems;Discrete Mathematics;Classical Analysis and ODEs