Local Methods in Nonlinear Differential Equations: Part I The Local Method of Nonlinear Analysis of Differential Equations Part II The Sets of Analyticity of a Normalizing Transformation - Rilegato

Bruno, Alexander D.

 
9783540189268: Local Methods in Nonlinear Differential Equations: Part I The Local Method of Nonlinear Analysis of Differential Equations Part II The Sets of Analyticity of a Normalizing Transformation
Rilegato
ISBN 10: 3540189262 ISBN 13: 9783540189268
Casa editrice: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1989

Sinossi

The method of normal forms is usually attributed to Poincaré although some of the basic ideas of the method can be found in earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno gives an account of the work of these mathematicians and further developments as well as the results of his own extensive investigations on the subject. The book begins with a thorough presentation of the analytical techniques necessary for the implementation of the theory as well as an extensive description of the geometry of the Newton polygon. It then proceeds to discuss the normal form of systems of ordinary differential equations giving many specific applications of the theory. An underlying theme of the book is the unifying nature of the method of normal forms regarding techniques for the study of the local properties of ordinary differential equations. In the second part of the book it is shown, for a special class of equations, how the method of normal forms yields classical results of Lyapunov concerning families of periodic orbits in the neighborhood of equilibrium points of Hamiltonian systems as well as the more modern results concerning families of quasiperiodic orbits obtained by Kolmogorov, Arnold and Moser. The book is intended for mathematicians, theoretical mechanicians, and physicists. It is suitable for advanced undergraduate and graduate students.

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Editore
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Data di pubblicazione
1989
Lingua
Inglese
ISBN 10 
3540189262
ISBN 13 
9783540189268
Rilegatura
Copertina rigida
Numero edizione
1
Numero di pagine
358
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
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Altre edizioni note dello stesso titolo

9780387189260: Local Methods in Nonlinear Differential Equations: Part I, the Local Method of Nonlinear Analysis of Differential Equations : Part Ii, the Sets of an

Edizione in evidenza

ISBN 10:  0387189262 ISBN 13:  9780387189260
Rilegato