Error distribution in randomly perturbed orbits

Ph Marie, G. Turchetti, S. Vaienti, F. Zanlungo

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Given an observable f defined on the phase space of some dynamical system generated by the map T, we consider the error between the value of the function f (Tn x0) computed at time n along the orbit with initial condition x0, and the value f (Tωn x 0) of the same observable computed by replacing the map Tn with the composition of maps T ωn T o⋯oT ω1, where each Tω is chosen randomly, by varying ω, in a neighborhood of size ε of T. We show that the random variable Δnε ≡ f (Tn x 0) -f (Tωn x0), depending on the initial condition x0 and on the choice of the realization ω, will converge in distribution when n→∞ to what we call the asymptotic error. We study in detail the density of the distribution function of the asymptotic error for a wide class of dynamical systems perturbed with additive noise: for a few of them we give rigorous results, for the others we provide a numerical investigation. Our study is intended as a model for the effects of numerical noise due to roundoff on dynamical systems.

Original languageEnglish
Article number043118
Issue number4
Publication statusPublished - 2009
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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