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Geometrical Methods in the Theory of Ordinary Differential Equations

  • Book
  • © 1988

Overview

Authors:
  1. V. I. Arnold

    1. Steklov Mathematical Institute, Moscow GSP-1, USSR

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 250)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Special Equations

    • V. I. Arnold
    Pages 1-58

  3. First-Order Partial Differential Equations

    • V. I. Arnold
    Pages 59-88

  4. Structural Stability

    • V. I. Arnold
    Pages 89-143

  5. Perturbation Theory

    • V. I. Arnold
    Pages 144-179

  6. Normal Forms

    • V. I. Arnold
    Pages 180-221

  7. Local Bifurcation Theory

    • V. I. Arnold
    Pages 222-341

  8. Back Matter

    Pages 342-353
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Keywords

About this book

Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, aswell as all users of the theory of differential equations.

Authors and Affiliations

  • Steklov Mathematical Institute, Moscow GSP-1, USSR

    V. I. Arnold

Bibliographic Information

  • Book Title: Geometrical Methods in the Theory of Ordinary Differential Equations

  • Authors: V. I. Arnold

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-1-4612-1037-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1988

  • Hardcover ISBN: 978-0-387-96649-6Published: 15 June 1988

  • Softcover ISBN: 978-1-4612-6994-6Published: 30 September 2012

  • eBook ISBN: 978-1-4612-1037-5Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 2

  • Number of Pages: XIII, 351

  • Additional Information: Title of the original Russian edition: Dopolnitel'nye teorii obyknovennych differencial'nych uravnenij

  • Topics: Analysis, Mathematics in Art and Architecture, Architectural History and Theory

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