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Tr. Mat. Inst. Steklova, 2005, Volume 250, Pages 198–218
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This article is cited in 27 scientific papers (total in 27 papers)
Capture into Resonance and Scattering on Resonances in Two-Frequency Systems
A. I. Neishtadt
Space Research Institute, Russian Academy of Sciences
Abstract:
Small perturbations imposed on an integrable system cause a slow evolution. During this evolution, the system may pass through a resonance state. In the paper, asymptotic formulas that describe associated phenomena, such as capture into a resonance and scattering by a resonance, are presented.
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Proceedings of the Steklov Institute of Mathematics, 2005, 250, 183–203
Bibliographic databases:
 
UDC:
531.36
Received in January 2005
Citation:
A. I. Neishtadt, “Capture into Resonance and Scattering on Resonances in Two-Frequency Systems”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 250, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 198–218; Proc. Steklov Inst. Math., 250 (2005), 183–203
Citation in format AMSBIB
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\by A.~I.~Neishtadt
\paper Capture into Resonance and Scattering on Resonances in Two-Frequency Systems
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2005
\vol 250
\pages 198--218
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm38}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200915}
\zmath{https://zbmath.org/?q=an:1127.34026}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 250
\pages 183--203
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Vainchtein D.L., Neishtadt A.I., Mezic I., “On passage through resonances in volume-preserving systems”, Chaos, 16:4 (2006), 043123, 11 pp.
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Vainchtein D.L., Widloski J., Grigoriev R.O., “Resonant chaotic mixing in a cellular flow”, Phys. Rev. Lett., 99:9 (2007), 094501, 4 pp.
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Makarov D.V., Uleysky M.Yu., “Giant acceleration in slow-fast space-periodic Hamiltonian systems”, Phys. Rev. E, 75:6 (2007), 065201, 4 pp.
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Delos J.B., Dhont G., Sadovskií D. A., Zhilinskií B.I., “Dynamical manifestation of Hamiltonian monodromy”, EPL, 83:2 (2008), 24003
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A. I. Neishtadt, “Averaging, passage through resonances, and capture into resonance in two-frequency systems”, Russian Math. Surveys, 69:5 (2014), 771–843
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Bazzani A., Frye Ch., Giovannozzi M., Hernalsteens C., “Analysis of Adiabatic Trapping For Quasi-Integrable Area-Preserving Maps”, Phys. Rev. E, 89:4 (2014), 042915
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