Abstract
We consider fast oscillating random perturbations of dynamical systems in regions where one can introduce action-angle-type coordinates. In an appropriate time scale, the evolution of first integrals, under the assumption that the set of resonance tori is small enough, is approximated by a diffusion process. If action-angle coordinates can be introduced only piece-wise, the limiting diffusion process should be considered on an open-book space. Such a process can be described by differential operators, one in each page, supplemented by some gluing conditions at the binding of the open book.
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Communicated by Eric A. Carlen.
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Freidlin, M.I., Wentzell, A.D. Diffusion Approximation for Noise-Induced Evolution of First Integrals in Multifrequency Systems. J Stat Phys 182, 45 (2021). https://doi.org/10.1007/s10955-021-02722-4
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DOI: https://doi.org/10.1007/s10955-021-02722-4