Arnold diffusion in a neighborhood of strong resonances

Arnold diffusion in a neighborhood of strong resonances

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...

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Veröffentlicht in:Proceedings of the Steklov Institute of Mathematics 2016-11, Vol.295 (1), p.63-94
Hauptverfasser: Davletshin, M. N., Treschev, D. V.
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Arnold diffusion
Hamiltonian functions
Mathematics
Mathematics and Statistics
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description 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.
doi_str_mv 10.1134/S0081543816080058
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subjects Arnold diffusion
Hamiltonian functions
Mathematics
Mathematics and Statistics
title Arnold diffusion in a neighborhood of strong resonances
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