Nonlinear Mechanics, Groups and Symmetry

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This text deals with the development of asymptotic methods of perturbation theory, making wide use of group theoretical techniques. Various assumptions about specific group properties are investigated and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincare-Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of lie groups is also treated. The examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems. This book should be of interestto researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering and biosciences.