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REFERENCES
1.
J. Guckenheimer & P.J. Holmes – Nonlinear Oscillations, Dynamical Systems and
Bifurcations of Vector Fields, Springer-Verlag, New York (1983).
2. V. I. Arnold - Geometrical Methods in the Theory of Ordinary Differential Equations,
Springer-Verlag Inc., New York (1988).
3. S. Wiggins – Introduction to Applied Nonlinear Dynamical Systems ad Chaos, SpringerVerlag, New York (1990).
4. Landau & Lifschitz - Mechanics, Pergamon Press.
5. V. I. Arnold - Ordinary Differential Equations, MIT Press, Cambridge, MA (1973).
6. A. D. Bruno - Local Methods in Nonlinear Differential Equations, Springer-Verlag,
Heidelberg (1989).
7. D. R. Smith - Singular Perturbation Theory, Cambridge University Press, New York
(1985).
8. P. B. Kahn – Mathematical Methods for Scientists and Engineers, Wiley (19909).
9. A. A. Nayfeh - Perturbation Methods, Wiley (1973); Introduction to Perturbation
techniques, Wiley (1981); Problems in Perturbation, Wiley (1985).
10. J. A. Murdock - Perturbations, Theory and Methods, Wiley (1991).
11. P.B. Kahn & Y. Zarmi – Nonlinear dynamics, Wiley, New York (1998).
1 – 5: Excellent general references.
10 – Introduction to perturbation ideas.
5, 6, 11 – Method of Normal Forms
9 – Method of Multiple Time Scales; Duffing oscillator in Poincaré-Lindstedt method
8 – Excellent collection of mathematical methods: excellent chapter on logistic equation, period
doubling and chaos.