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Stochasticity in many-dimensional nonlinear oscillating systems

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Abstract

Qualitative analytic estimates of the stochasticity limit of one- and many-dimensional nonlinear oscillating systems are derived using the overlapping of first-order resonances as a criterion for stochasticity. Computational results obtained with several very simple transformations are compared with the analytic estimates. Numerical studies significantly below the stochasticity limit of a many-dimensional nonlinear system reveal an example of a very slow instability, the first, to the best of our knowledge.

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Authors and Affiliations

  1. Institute of Nuclear Physics, Novosibirsk, USSR

    B. V. Chirikov

  2. ISR Division, CERN, Geneva, Switzerland

    E. Keil

  3. Lawrence Radiation Laboratory, Berkeley, California

    A. M. Sessler

Authors
  1. B. V. Chirikov
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  2. E. Keil
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  3. A. M. Sessler
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Chirikov, B.V., Keil, E. & Sessler, A.M. Stochasticity in many-dimensional nonlinear oscillating systems. J Stat Phys 3, 307–321 (1971). https://doi.org/10.1007/BF01011386

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  • DOI: https://doi.org/10.1007/BF01011386

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