On Phase at a Resonance in Slow-Fast Hamiltonian Systems

Regular and Chaotic Dynamics - Tập 28 Số 4-5 - Trang 585-612 - 2023
Yuyang Gao1, A. I. Neishtadt1, A. G. Okunev2
1Dept. of Math. Sciences, Loughborough University, Loughborough, LE11 3TU, Leicestershire, UK
2Pennsylvania State University, State College, Pennsylvania, United States

Tóm tắt

Từ khóa


Tài liệu tham khảo

Arnol’d, V. I., Mathematical Methods of Classical Mechanics, 2nd ed., Grad. Texts in Math., vol. 60, New York: Springer, 1997.

Arnol’d, V. I., Small Denominators and Problems of Stability of Motion in Classical and Celestial Mechanics, Russian Math. Surveys, 1963, vol. 18, no. 6, pp. 85–191; see also: Uspekhi Mat. Nauk, 1963, vol. 18, no. 6(114), pp. 91-192.

Arnol’d, V. I., Kozlov, V. V., and Neĭshtadt, A. I., Mathematical Aspects of Classical and Celestial Mechanics, 3rd ed., Encyclopaedia Math. Sci., vol. 3, Berlin: Springer, 2006.

Artemyev, A. V., Neishtadt, A. I., and Vasiliev, A. A., Mapping for Nonlinear Electron Interaction with Whistler-Mode Waves, Phys. Plasmas, 2020, vol. 27, no. 4, 042902, 12 pp.

Bogoliubov, N. N. and Mitropolsky, Yu. A., Asymptotic Methods in the Theory of Non-Linear Oscillations, New York: Gordon & Breach, 1961.

Brothers, J. D. and Haberman, R., Accurate Phase after Slow Passage through Subharmonic Resonance, SIAM J. Appl. Math., 1999, vol. 59, no. 1, pp. 347–364.

Fenichel, N., Geometric Singular Perturbation Theory for Ordinary Differential Equations, J. Differential Equations, 1979, vol. 31, no. 1, pp. 53–98.

Chirikov, B. V., Passage of Nonlinear Oscillatory System through Resonance, Sov. Phys. Dokl., 1959, vol. 4, pp. 390–394; see also: Dokl. Akad. Nauk SSSR, 1959, vol. 125, no. 5, pp. 1015-1018.

Goldreich, G. and Peale, S., Spin-Orbit Coupling in the Solar System, Astron. J., 1966, vol. 71, no. 6, pp. 425–438.

Kevorkian, J., On a Model for Reentry Roll Resonance, SIAM J. Appl. Math., 1974, vol. 26, no. 3, pp. 638–669.

Kiselev, O. M. and Tarkhanov, N., The Capture of a Particle into Resonance at Potential Hole with Dissipative Perturbation, Chaos Solitons Fractals, 2014, vol. 58, pp. 27–39.

Lifshits, I. M., Slutskin, A. A., and Nabutovskii, V. M., The “Scattering” of Charged Quasi-Particles from Singularities in $$p$$-Space, Soviet Phys. Dokl., 1961, vol. 6, pp. 238–240; see also: Dokl. Akad. Nauk, 1961, vol. 137, no. 3, pp. 553-556.

Neishtadt, A. I., Scattering by Resonances, Celestial Mech. Dynam. Astronom., 1996/97, vol. 65, no. 1–2, pp. 1–20.

Neishtadt, A. I., Capture into Resonance and Scattering on Resonances in Two-Frequency Systems, Proc. Steklov Inst. Math., 2005, vol. 250, pp. 183–203; see also: Tr. Mat. Inst. Steklova, 2005, vol. 250, pp. 198-218.

Neishtadt, A., Averaging Method for Systems with Separatrix Crossing, Nonlinearity, 2017, vol. 30, no. 7, pp. 2871–2917.

Neishtadt, A. and Vasiliev, A., Phase Change between Separatrix Crossings in Slow-Fast Hamiltonian Systems, Nonlinearity, 2005, vol. 18, no. 3, pp. 1393–1406.

Neishtadt, A. and Okunev, A., Phase Change and Order $$2$$ Averaging for One-Frequency Systems with Separatrix Crossing, Nonlinearity, 2022, vol. 35, no. 8, pp. 4469–4516.