The stochastic properties of classical dynamical systems are often studied by means of numerical computations of orbits up to very large times, so that the accumulation of numerical errors would appear to destroy the reliability of the computations. We discuss this problem on the basis of a theorem of Anosov and Bowen which implies that, if the errors at each step are small enough, for Anosov systems the computations of time averages are reliable even for infinite times. We test numerically from this point of view three classical examples.
On the reliability of numerical studies of stochasticity I: Existence of time averages
BENETTIN, GIANCARLO;
1978
Abstract
The stochastic properties of classical dynamical systems are often studied by means of numerical computations of orbits up to very large times, so that the accumulation of numerical errors would appear to destroy the reliability of the computations. We discuss this problem on the basis of a theorem of Anosov and Bowen which implies that, if the errors at each step are small enough, for Anosov systems the computations of time averages are reliable even for infinite times. We test numerically from this point of view three classical examples.
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