Graduate Studies in Mathematics Yulij Ilyashenko Sergei Yakovenko Lectures on analytic differenti...
Graduate Studies in Mathematics Yulij Ilyashenko Sergei Yakovenko Lectures on analytic differential equations American Mathematical Society 2007 | 2.57 MB
English | 349 Pages| ISBN: 978-0821836675
Title: Lectures on Analytic Differential Equations
Author: Yulij Ilyashenko and Sergei Yakovenko
Year: 2007
Description:
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 (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 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.
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https://rapidgator.net/file/d52469058e7e3eba0097ac3b52afed5c/Graduate_Studies_in_Mathematics_Yulij_Ilyashenko_Sergei_Yakovenko_Lectures_on_analytic_differential_equations_American_Mathematical_Society_2007.rar
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 (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 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.
DOWNLOAD:
https://rapidgator.net/file/d52469058e7e3eba0097ac3b52afed5c/Graduate_Studies_in_Mathematics_Yulij_Ilyashenko_Sergei_Yakovenko_Lectures_on_analytic_differential_equations_American_Mathematical_Society_2007.rar
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