Abstract
We consider the problem of convergence towards spatial ergodic average of the time average of an observable defined for a one and a half degree of freedom Hamiltonian flow with mixed phase space. The analysis is performed by analysing the evolution of the distribution of finite-time averages. An exponent characterising the “speed of convergence” is defined. Results indicate that for the considered mixed case, the rate of convergence goes as t α , with α = 0.45 while it goes as t 1 / 2 when the full phase space is chaotic. Moreover a formula linking this characteristic exponent to the one corresponding to transport properties β is proposed α = 1 − β / 2 and good agreement is found for the considered cases. To cite this article: X. Leoncini et al., C. R. Mecanique 336 (2008).
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