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11.5 Guide to the Literature
Bogoliubov, N.N. and Mitropolsky, Yu.A. (1961), Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York.
Cochran, J.A. (1962), Problems in Singular Perturbation Theory, Stanford University, Stanford, CA.
Kevorkian, J.K. (1961), The uniformly valid asymptotic representation of the solution of certain nonlinear differential equations, California Institute of Technology, Pasadena.
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.
Kuzmak, G.E. (1959), Asymptotic solutions of nonlinear second order differential equations with variable coefficients, J. Appl. Math. Mech. (PMM) 10, pp. 730–744.
Lagrange, J.L. (1788), Mécanique Analytique (2 vols.), Paris (reprinted by Blanchard, Paris, 1965).
Mahony, J.J. (1962), An expansion method for singular perturbation problems, J. Austr. Math. Soc. 2, pp. 440–463.
Mitropolsky, Yu.A. (1981), private communication at seminar, Mathematics Institute, Kiev.
Nayfeh, A.H. (1973), Perturbation Methods, Wiley-Interscience, New York.
Poincaré, H. (1892, 1893, 1899), Les Méthodes Nouvelles de la Mécanique Céleste, 3 vols., Gauthier-Villars, Paris.
Sanders, J.A. and Verhulst, F. (1985), Averaging Methods in Nonlinear Dynamical Systems, Applied Mathematical Sciences 59, Springer-Verlag, New York.
Verhulst, F. (2000), Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer-Verlag, New York.
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(2005). Averaging and Timescales. In: Methods and Applications of Singular Perturbations. Texts in Applied Mathematics, vol 50. Springer, New York, NY. https://doi.org/10.1007/0-387-28313-7_11
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