Normal Forms and Unfoldings for Local Dynamical Systems (Springer Monographs in Mathematics) - Softcover

Murdock, James

Softcover

ISBN 10: 1441930132 ISBN 13: 9781441930132

Verlag: Springer, 2010

Inhaltsangabe

The goal of this book is to present the most thorough treatment of normal forms that currently exists in book form. Presently there is a big gap between the elementary treatments in textbooks and the advanced research papers on normal forms. The targeted audience for this book is Ph.D. students and researchers in applied mathematics, theoretical physics, and advanced engineering. While it is self- contained and could in principle be read by anyone with a sufficient background in linear algebra and differential equations, it is assumed that most readers will have had some previous exposure to dynamical systems.

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From the reviews:

"In the analysis of local dynamical systems ... normal form theory plays an essential role. ... this is a serious introduction to methods that have been developed in the last few decades. ... This is a book that can be enjoyed on many levels, which is bound to give the reader new insights into the theory of normal forms and its applications." (Jan A. Sanders, Mathematical Reviews, Issue 2003 k)

"The book ... aims to introduce both the algebraic structure of the coordinate transformations that are used in the normalization and ... the geometric structure of the vector fields that are thus obtained. ... The discussion ... is the most lucid I have found to date. ... The reader who expects to learn the basic ideas and techniques of normal form theory will find this book rewarding. Its algebraic approach is well suited to readers interested in automated computations of normal forms." (Kresimir Josic, Siam Review, Vol. 46 (4), 2004)

"Normal-form theory has become a celebrated topic which is widely used in nonlinear science. ... This book certainly represents a very thorough treatment of the anatomy of normal-form transformations ... . It may serve well as a reference work ... and indeed the author achieves his stated aim of providing an encyclopedia of results and explanations which are not easily found in the existing literature." (Mark Groves, UK Nonlinear News, Issue 35, February, 2004)

"The theory of local dynamical systems studies neighbourhoods of a given equilibrium point, in particular the dynamical behaviour that is generically possible. ... To my knowledge the monograph under review is the first successful attempt to deal with the ‘Elphick-Iooss’ inner product style and the ‘Cushman-Sanders’ sl(2) style at a larger scale. ... the text successfully addresses computer-algebraic aspects of certain normal form computations that are useful for applications in concrete examples." (Henk Broer, Siam, November, 2003)

"This book is a treatise on normal forms and unfoldings of a dynamical system near a singular point. The goal is to lay down basic principles and this is ... the main originality of this work. Moreover it is selfcontained. ... The volume contains new results including some of the author. ... This conceptually attractive and clearly written book is recommended." (A. Akutowicz, Zentralblatt MATH, Vol. 1014, 2003)

Reseña del editor

This is the most thorough treatment of normal forms currently existing in book form. There is a substantial gap between elementary treatments in textbooks and advanced research papers on normal forms. This book develops all the necessary theory 'from scratch' in just the form that is needed for the application to normal forms, with as little unnecessary terminology as possible.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 1441930132
• ISBN 13: 9781441930132
• Einband: Tapa blanda
• Anzahl der Seiten: 516
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland