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Tr. Mat. Inst. Steklova, 2005, Volume 250, Pages 198–218 (Mi tm38)  

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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English version:
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
\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.
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 250
\pages 183--203

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    This publication is cited in the following articles:
    1. Vainchtein D.L., Neishtadt A.I., Mezic I., “On passage through resonances in volume-preserving systems”, Chaos, 16:4 (2006), 043123, 11 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Neishtadt A.I., Vasiliev A.A., “Destruction of adiabatic invariance at resonances in slow-fast Hamiltonian systems”, Nuclear Instruments and Methods in Physics Research Section A, 561:2 (2006), 158–165  crossref  adsnasa  isi  scopus
    3. Kon'kov L.E., Makarov D.V., Sosedko E.V., Uleysky M.Yu., “Recovery of ordered periodic orbits with increasing wavelength for sound propagation in a range-dependent waveguide”, Phys. Rev. E, 76:5 (2007), 056212, 9 pp.  crossref  adsnasa  isi  scopus
    4. Vainchtein D.L., Widloski J., Grigoriev R.O., “Resonant chaotic mixing in a cellular flow”, Phys. Rev. Lett., 99:9 (2007), 094501, 4 pp.  crossref  adsnasa  isi  elib  scopus
    5. Makarov D.V., Uleysky M.Yu., “Giant acceleration in slow-fast space-periodic Hamiltonian systems”, Phys. Rev. E, 75:6 (2007), 065201, 4 pp.  crossref  adsnasa  isi  elib  scopus
    6. Celletti A., Froeschle C., Lega E., “Dynamics of the conservative and dissipative spin–orbit problem”, Planetary and Space Science, 55:7-8 (2007), 889–899  crossref  isi  scopus
    7. Makarov D.V., Uleysky M.Yu., “Resonant influence of spatial oscillations of a perturbation on motion of a nonlinear oscillator”, Nonlinear Science and Complexity, Transactions of Nonlinear Science and Complexity, 1, 2007, 54–61  crossref  mathscinet  zmath  isi
    8. Vainchtein D.L., Widloski J., Grigoriev R.O., “Resonant mixing in perturbed action-action-angle flow”, Phys. Rev. E (3), 78:2 (2008), 026302, 11 pp.  crossref  mathscinet  adsnasa  isi  scopus
    9. Delos J.B., Dhont G., Sadovskií D. A., Zhilinskií B.I., “Dynamical manifestation of Hamiltonian monodromy”, EPL, 83:2 (2008), 24003  crossref  mathscinet  adsnasa  isi  elib  scopus
    10. Makarov D.V., Kon'kov L.E., Uleysky M.Yu., “The ray-wave correspondence and the suppression of chaos in long-range sound propagation in the ocean”, Acoustical Physics, 54:3 (2008), 382–391  crossref  adsnasa  isi  elib  scopus
    11. Makarov D.V., Uleysky M.Yu., “Local chaos induced by spatial oscillations of a perturbation”, Commun. Nonlinear Sci. Numer. Simul., 13:2 (2008), 400–406  crossref  zmath  adsnasa  isi  elib  scopus
    12. Neishtadt A., “Averaging method and adiabatic invariants”, Hamiltonian Dynamical Systems and Applications, NATO Science for Peace and Security Series B - Physics and Biophysics, 2008, 53–66  crossref  mathscinet  zmath  isi
    13. Neishtadt A., Vainchtein D., Vasiliev A., “Adiabatic invariance in volume-preserving systems”, Iutam Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Iutam Bookseries, 6, 2008, 89–107  crossref  mathscinet  zmath  isi
    14. Vainchtein D.L., Vasiliev A.A., Neishtadt A.I., “Electron dynamics in a parabolic magnetic field in the presence of an electrostatic wave”, Plasma Physics Reports, 35:12 (2009), 1021–1031  crossref  adsnasa  isi  elib  scopus
    15. Neishtadt A., Vainchtein D., Vasiliev A., “Dynamics of Electrons in a Parabolic Magnetic Field Perturbed by an Electromagnetic Wave”, Plasma Phys. Control. Fusion, 53:8 (2011), 085014  crossref  adsnasa  isi  elib  scopus
    16. A. L. Virovlyansky, D. V. Makarov, S. V. Prants, “Ray and wave chaos in underwater acoustic waveguides”, Phys. Usp., 55:1 (2012), 18–46  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    17. S. B. Kuksin, A. I. Neishtadt, “On quantum averaging, quantum KAM, and quantum diffusion”, Russian Math. Surveys, 68:2 (2013), 335–348  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. A. I. Neishtadt, “Averaging, passage through resonances, and capture into resonance in two-frequency systems”, Russian Math. Surveys, 69:5 (2014), 771–843  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. Guan H., Kuksin S., “the KdV Equation Under Periodic Boundary Conditions and Its Perturbations”, Nonlinearity, 27:9 (2014), R61–R88  crossref  mathscinet  zmath  isi  scopus
    20. 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  crossref  isi  elib  scopus
    21. Artemyev A.V., Vasiliev A.A., Mourenas D., Neishtadt A.I., Agapitov O.V., Krasnoselskikh V., “Probability of Relativistic Electron Trapping By Parallel and Oblique Whistler-Mode Waves in Earth's Radiation Belts”, Phys. Plasmas, 22:11 (2015), 112903  crossref  adsnasa  isi  elib  scopus
    22. Lhotka C., Celletti A., Gales C., “Poynting?Robertson drag and solar wind in the space debris problem”, Mon. Not. Roy. Astron. Soc., 460:1 (2016), 802–815  crossref  isi  elib  scopus
    23. Fidlin A., Drozdetskaya O., “On the Averaging in Strongly Damped Systems: The General Approach and its Application to Asymptotic Analysis of the Sommerfeld Effect”, Iutam Symposium Analytical Methods in Nonlinear Dynamics, Procedia Iutam, 19, eds. Hagedorn P., Clerkin E., Elsevier Science BV, 2016, 43–52  crossref  isi  scopus
    24. L. A. Kalyakin, “Uravnenie Penleve-II kak model rezonansnogo vzaimodeistviya ostsillyatorov”, Tr. IMM UrO RAN, 23, no. 2, 2017, 104–116  mathnet  crossref  elib
    25. L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, Theoret. and Math. Phys., 194:3 (2018), 331–346  mathnet  crossref  crossref  isi  elib
    26. Drozdetskaya O., Fidlin A., “On the Passing Through Resonance of a Centrifugal Exciter With Two Coaxial Unbalances”, Eur. J. Mech. A-Solids, 72 (2018), 516–520  crossref  mathscinet  zmath  isi  scopus
    27. L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufa Math. J., 10:4 (2018), 64–76  mathnet  crossref  isi
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