© 1988

Geometrical Methods in the Theory of Ordinary Differential Equations


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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. V. I. Arnold
    Pages 1-58
  3. V. I. Arnold
    Pages 89-143
  4. V. I. Arnold
    Pages 144-179
  5. V. I. Arnold
    Pages 180-221
  6. V. I. Arnold
    Pages 222-341
  7. Back Matter
    Pages 342-353

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, as well as all users of the theory of differential equations.


Mathematica bifurcation differential equation hamiltonian system ordinary differential equation partial differential equation schrödinger equation stability

Authors and affiliations

  1. 1.Steklov Mathematical InstituteMoscow GSP-1USSR

Bibliographic information

  • Book Title Geometrical Methods in the Theory of Ordinary Differential Equations
  • Authors V.I. Arnold
  • Editors Mark Levi
  • Series Title Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag New York Inc. 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-96649-6
  • Softcover ISBN 978-1-4612-6994-6
  • eBook ISBN 978-1-4612-1037-5
  • Series ISSN 0072-7830
  • Edition Number 2
  • Number of Pages XIII, 351
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • 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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