In the numerical study of classical dynamical systems presenting stochastic behaviour one frequently makes use, in an explicit or an implicit way, of the Birkhoff ergodic theorem. The correct interpretation of the obtained results presents some delicate problems related to the coexistence of many mutually singular invariant measures. In this paper we study this question in an experimental way on some simple model examples.
On the reliability of numerical studies of stochasticity
BENETTIN, GIANCARLO;
1979
Abstract
In the numerical study of classical dynamical systems presenting stochastic behaviour one frequently makes use, in an explicit or an implicit way, of the Birkhoff ergodic theorem. The correct interpretation of the obtained results presents some delicate problems related to the coexistence of many mutually singular invariant measures. In this paper we study this question in an experimental way on some simple model examples.
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