Hardcover ISBN:  9780821836675 
Product Code:  GSM/86 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470421168 
Product Code:  GSM/86.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821836675 
eBook: ISBN:  9781470421168 
Product Code:  GSM/86.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9780821836675 
Product Code:  GSM/86 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470421168 
Product Code:  GSM/86.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821836675 
eBook ISBN:  9781470421168 
Product Code:  GSM/86.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 86; 2008; 625 ppMSC: Primary 34; Secondary 14; 32; 13
The book combines the features of a graduatelevel textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes selfcontained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann–Hilbert problem, Ecalle–Voronin and Martinet–Ramis moduli, solution of the Poincaré problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text.
The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.
ReadershipGraduate students and research mathematicians interested in analysis and geometry of differential equations in real and complex domain.

Table of Contents

Chapters

Chapter I. Normal forms and desingularization

Chapter II. Singular points of planar analytic vector fields

Chapter III. Local and global theory of linear systems

Chapter IV. Functional moduli of analytic classification of resonant germs and their applications

Chapter V. Global properties of complex polynomial foliations

First aid


Additional Material

Reviews

The authors provide a crash course on functions of several complex variables and elements of the theory of Riemann spaces.
Mathematical Horizon 
The book is easy to read. The ideas and directions are clearly indicated before going into details. ... Moreover, it is easy to open the book at any section and start reading.
Mathematical Reviews


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The book combines the features of a graduatelevel textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes selfcontained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann–Hilbert problem, Ecalle–Voronin and Martinet–Ramis moduli, solution of the Poincaré problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text.
The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.
Graduate students and research mathematicians interested in analysis and geometry of differential equations in real and complex domain.

Chapters

Chapter I. Normal forms and desingularization

Chapter II. Singular points of planar analytic vector fields

Chapter III. Local and global theory of linear systems

Chapter IV. Functional moduli of analytic classification of resonant germs and their applications

Chapter V. Global properties of complex polynomial foliations

First aid

The authors provide a crash course on functions of several complex variables and elements of the theory of Riemann spaces.
Mathematical Horizon 
The book is easy to read. The ideas and directions are clearly indicated before going into details. ... Moreover, it is easy to open the book at any section and start reading.
Mathematical Reviews