Abstract
We estimate the rate at which the image of a point fills the flat Euclidean α-torus when subjected to linear flow satisfying certain nonresonance or near-nonresonance conditions arising naturally in perturbation theory for ODEs. The estimates are explicit and display dependence on all relevant parameters but are not sharp. These results were used to estimate the maximum time until near-collision with nuclei for highly energetic charged particles traveling through crystals in directions “far from channeling directions” and are presented here with complete proofs.
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Dumas, H.S. Ergodization rates for linear flow on the torus. J Dyn Diff Equat 3, 593–610 (1991). https://doi.org/10.1007/BF01049101
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DOI: https://doi.org/10.1007/BF01049101