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Lectures on analytic differential equations

Author: Yulij Ilyashenko, Sergei Yakovenko
Url: http://www.wisdom.weizmann.ac.il/~yakov/book-titlepage.htm
Format: Pdf
Category: Differential Equations
Pages: 599
Clicks: 1336

The first chapter contains the basics of formal and analytic normal form theory. The tools developed in this chapter are systematically used throughout the book. In the Chapter II we treat a new approach to local problems of analysis, based on the notion of algebraic and analytic solvability, was suggested by V. Arnold and R. Thom around thirty years ago, from this point of view the local theory of singular points of planar vector fields. The third chapter deal with the linear theory. Chapter IV deals with a new direction in the thoery of normal forms the functional moduli of analytic classification of resonant singularities. The fifth chapter is concerned with the global theory of polynomial differential equations on the real and complex plane, bridging between algebraic, ‘almost algebraic’ and essentially transcendental questions.

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