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Lectures On Analytic Differential Equations (Graduate Studies In Mathematics)

The book combines the features of a graduate-level 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 self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (...

Series: Graduate Studies in Mathematics (Book 86)
Hardcover: 625 pages
Publisher: American Mathematical Society (December 27, 2007)
Language: English
ISBN-10: 0821836676
ISBN-13: 978-0821836675
Product Dimensions: 7 x 1.5 x 10 inches
Amazon Rank: 1839461
Format: PDF Text TXT book

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“This book of professors Ilyashenko and Yacovenko is like a kind of encyclopedia of recent develop theory on differential equations, contains the most important new results in this field....”

esingularization 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 Poincare 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.