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Long-Time Behavior of Weakly Coupled Oscillators

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We consider small perturbations of a simple completely integrable system with many degrees of freedom: a collection of independent one-degree-of-freedom oscillators (in the perturbed system the individual oscillators are no longer independent). We show that the long-time behavior of such a system, even in the case of purely deterministic perturbations, should, in general, be described as a stochastic process. The limiting stochastic process is a Markov process on an open book space corresponding to the collection of first integrals of the non-perturbed system.

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Authors and Affiliations

  1. University of Maryland, College Park, USA

    M. I. Freidlin

  2. Tulane University, New Orleans, USA

    A. D. Wentzell

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  1. M. I. Freidlin
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  2. A. D. Wentzell
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Correspondence to M. I. Freidlin.

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Freidlin, M.I., Wentzell, A.D. Long-Time Behavior of Weakly Coupled Oscillators. J Stat Phys 123, 1311–1337 (2006). https://doi.org/10.1007/s10955-006-9133-8

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  • DOI: https://doi.org/10.1007/s10955-006-9133-8

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