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Normal Forms and Unfoldings for Local Dynamical Systems (eBook, PDF)

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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.

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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