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Symmetry and Perturbation Theory in Nonlinear Dynamics

✍ Scribed by Giampaolo Cicogna, Guiseppe Gaeta

Book ID
127434167
Publisher
Springer
Year
1999
Tongue
English
Weight
3 MB
Series
Lecture notes in physics. Monographs m57
Edition
1
Category
Library
City
Berlin; New York
ISBN
3540659048
ISSN
0940-7677

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✦ Synopsis

This book deals with the theory of PoincarΓ© - Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly. Some results on the simultaneous normalization of a vector field describing a dynamical system and vector fields describing its symmetry are presented and perturbative approach is also used. Attention is given to the problem of convergence of the normalizing transformation in the presence of symmetry, with some other extensions of the theory. The results are discussed for the general case of dynamical systems and also for the specific Hamiltonian setting.

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