Geodesic
Arnold diffusion in a~neighborhood of strong resonances
Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 72-106

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2016_295_a4,
     author = {M. N. Davletshin and D. V. Treschev},
     title = {Arnold diffusion in a~neighborhood of strong resonances},
     journal = {Informatics and Automation},
     pages = {72--106},
     publisher = {mathdoc},
     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a4/}
}
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M. N. Davletshin; D. V. Treschev. Arnold diffusion in a~neighborhood of strong resonances. Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 72-106. http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a4/