This book deals with the theory of Poincar --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 a 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...

Si tratta di un libro di testo per i corsi di Matematica delle lauree specialistiche della classe di Biologia e Scienze Naturali. Sara di interesse anche per studenti dello stesso livello in Scienze Ambientali ed anche di Medicina. Potrebbe essere usato (in particolare i suoi capitoli piu' avanzati, segnatamente quelli che trattano la teoria dell'evoluzione) anche come testo complementare per corsi di Biomatematica.

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The third conference (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field - more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit.

Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and Schrodinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDEs (G Cicogna); Bifurcations in Flow-Induced Vibrations (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Y Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); On the Algebro Geometric Solution of a 3x3...

This text serves as an introduction to the use of nonlinear symmetries in studying, simplifying and solving nonlinear equations. Part One provides a self-contained introduction to the theory. This emphasizes an intuitive understanding of jet spaces and the geometry of differential equations, and a special treatment of evolution problems and dynamical systems, including original results. In Part Two the theory is applied to equivariant dynamics, to bifurcation theory and to gauge symmetries, reporting recent results by the author. In particular, the fundamental results of equivariant...