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Arnold diffusion in a neighborhood of strong resonances

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Abstract

The paper deals with nearly integrable multidimensional a priori unstable Hamiltonian systems. Assuming the Hamilton function is smooth and time-periodic, we study perturbations that are trigonometric polynomials in the “angle” variables in the first approximation. For a generic system in this class, we construct a trajectory whose projection on the space of slow variables crosses a small neighborhood of a strong resonance. We also estimate the speed of this crossing.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    M. N. Davletshin & D. V. Treschev

Authors
  1. M. N. Davletshin
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  2. D. V. Treschev
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Correspondence to M. N. Davletshin.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 295, pp. 72–106.

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Davletshin, M.N., Treschev, D.V. Arnold diffusion in a neighborhood of strong resonances. Proc. Steklov Inst. Math. 295, 63–94 (2016). https://doi.org/10.1134/S0081543816080058

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  • DOI: https://doi.org/10.1134/S0081543816080058

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