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Article Dans Une Revue Journal de Physique Année : 1984

Chaos, pseudo-random number generators and the random walk problem

D. Sornette
  • Fonction : Auteur
A. Arneodo

Résumé

To test the nature of the deterministic chaos generated by the iteration of discrete dynamical systems, we perform Monte-Carlo random walk experiments on a one-dimensional periodic lattice with a trapping site using the logistic map as a generator of pseudo-random numbers. Comparison with analytical results derived for asymmetric and also for weakly non-Markovian random walks lend strong experimental support to the conjecture that sensitive dependence on the initial conditions implies for the map the existence of an absolutely continuous invariant measure with respect to Lebesgue's measure.

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Dates et versions

jpa-00209929 , version 1 (04-02-2008)

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D. Sornette, A. Arneodo. Chaos, pseudo-random number generators and the random walk problem. Journal de Physique, 1984, 45 (12), pp.1843-1857. ⟨10.1051/jphys:0198400450120184300⟩. ⟨jpa-00209929⟩

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