The method of normal forms

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In this introductory treatment, Ali Nayfeh presents concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet straightforward manner. He systematically introduces models and techniques, clearly stating their ranges of validity and applicability. The reader is provided with a clear operational framework for practical use, rather than an emphasis on the underlying mathematical details. The exposition largely relies on examples, leading to their final outcomes. For many examples, results obtained through the method of normal forms are equivalent to those from other perturbation methods, such as multiple scales and averaging. The previous edition garnered significant attention from researchers globally in the field of nonlinear dynamics and its engineering applications. This new edition includes major topics of current interest, featuring three new chapters on Maps, Bifurcations of Continuous Systems, and Retarded Systems, the latter of which has gained importance in various applications across mechanics and other areas. The content is accessible to engineers and applied scientists engaged with nonlinear dynamics in diverse fields. A basic knowledge of calculus and the elementary properties of ordinary differential equations is assumed for readers.