Summary
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.
Riassunto
Nello studio numerico dei sistemi dinamici classici che presentano comportamento stocastico si fa spesso uso, esplicitamente o implicitamente, del teorema ergodico di Birkhoff. L’interpretazione corretta dei risultati che si ottengono presenta dei problemi delicati connessi alla coesistenza di molte misure invarianti mutuamente singolari. In questo lavoro si studia tale problema da un punto di vista sperimentale su alcuni semplici esempi modello.
Резюме
При численном исследовании классических динамических систем, обладающих стохастическим поведением, часто используется эргодическая теорема Биркхофа. Правильная интерпретация полученных результатов представляет довольно деликатную проблему. В этой статье мы исследуем эту провлему экспериментальным путем на примерах некоторых простых моделей.
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Benettin, G., Casartelli, M., Galgani, L. et al. On the reliability of numerical studies of stochasticity. Nuov Cim B 50, 211–232 (1979). https://doi.org/10.1007/BF02748874
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DOI: https://doi.org/10.1007/BF02748874