• ### Asymptotic Frequencies of Bounded Differential Equations

guy Cirier

LSTA, University Pierre et Marie Curie Sorbonne, France.

Abstract: We study an ordinary differential equation as an iteration with a constant fixed path when the number of iterations goes to infinite. In such conditions, very different from these of classical analysis, we greatly increase the spectrum of the solutions. First, we treat this iteration in a probabilistic framework. Curves where the probability of presence is invariant are shown. There are also critical frequencies but their interpretation remains difficult.

Keywords: Invariant measures, Perron-Frobénius, function of Plancherel – Rotach, steepest descent’s method, Lorenz’s attractor, critical frequencies.