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Averaging and Timescales

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Part of the Texts in Applied Mathematics book series (TAM, volume 50)

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11.5 Guide to the Literature

  1. 14.
    Bogoliubov, N.N. and Mitropolsky, Yu.A. (1961), Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York.Google Scholar
  2. 33.
    Cochran, J.A. (1962), Problems in Singular Perturbation Theory, Stanford University, Stanford, CA.Google Scholar
  3. 102.
    Kevorkian, J.K. (1961), The uniformly valid asymptotic representation of the solution of certain nonlinear differential equations, California Institute of Technology, Pasadena.Google Scholar
  4. 110.
    Kryloff, N. and Bogoliubov, N. (1935), Méthodes approchées de la mécanique non linéaire dans leur application dans l’étude de la perturbation des mouvements périodiques et de divers phénomènes de résonance s’y rapportant, Acad. Sci. Ukraine 14.Google Scholar
  5. 112.
    Kuzmak, G.E. (1959), Asymptotic solutions of nonlinear second order differential equations with variable coefficients, J. Appl. Math. Mech. (PMM) 10, pp. 730–744.CrossRefMathSciNetGoogle Scholar
  6. 114.
    Lagrange, J.L. (1788), Mécanique Analytique (2 vols.), Paris (reprinted by Blanchard, Paris, 1965).Google Scholar
  7. 130.
    Mahony, J.J. (1962), An expansion method for singular perturbation problems, J. Austr. Math. Soc. 2, pp. 440–463.CrossRefMathSciNetGoogle Scholar
  8. 136.
    Mitropolsky, Yu.A. (1981), private communication at seminar, Mathematics Institute, Kiev.Google Scholar
  9. 140.
    Nayfeh, A.H. (1973), Perturbation Methods, Wiley-Interscience, New York.zbMATHGoogle Scholar
  10. 153.
    Poincaré, H. (1892, 1893, 1899), Les Méthodes Nouvelles de la Mécanique Céleste, 3 vols., Gauthier-Villars, Paris.Google Scholar
  11. 166.
    Sanders, J.A. and Verhulst, F. (1985), Averaging Methods in Nonlinear Dynamical Systems, Applied Mathematical Sciences 59, Springer-Verlag, New York.Google Scholar
  12. 212.
    Verhulst, F. (2000), Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer-Verlag, New York.Google Scholar

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