Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems

N. G. Moshchevitin

Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 394-410.

Résumé

The asymptotic behavior of mean values for integrals of quasiperiodic functions, which characterizes the uniformity of the distribution of irrational windings on a torus, is shown to be essentially dependent on the dimension of the torus. We prove the nonrecurrence of mean values for arbitrarily smooth three-frequency quasiperiodic functions. We also present a series of results concerning the distribution of fractional parts for systems of linear functions.

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