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First approach of invariant densities of a Perron Frobenius operator.Asymptotic behaviours of ODE or PDE, as, are most interesting. The associedinfinitesimal iteration is. If is partially linear, a random distribution canbe asymptotic solution. Among applications, are asymptotic profiles of ofLorenz, Navier Stokes or Hamilton's \'equations.

Premi\`ere approche de la densit\'e d'un op\'erateur de Perron Frobenius. III - Applications : EDP, EDO, etc