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Introduction to Structurally Stable Systems of Differential Equations

  • Sergei Yu. Pilyugin

Table of contents

  1. Front Matter
    Pages i-xi
  2. Sergei Yu. Pilyugin
    Pages 1-9
  3. Sergei Yu. Pilyugin
    Pages 10-16
  4. Sergei Yu. Pilyugin
    Pages 23-46
  5. Sergei Yu. Pilyugin
    Pages 47-56
  6. Sergei Yu. Pilyugin
    Pages 57-72
  7. Sergei Yu. Pilyugin
    Pages 73-86
  8. Sergei Yu. Pilyugin
    Pages 87-91
  9. Sergei Yu. Pilyugin
    Pages 92-99
  10. Sergei Yu. Pilyugin
    Pages 100-107
  11. Sergei Yu. Pilyugin
    Pages 108-118
  12. Sergei Yu. Pilyugin
    Pages 119-156
  13. Sergei Yu. Pilyugin
    Pages 157-173
  14. Back Matter
    Pages 175-188

About this book

Introduction

This book is based on a one year course of lectures on structural sta­ bility of differential equations which the author has given for the past several years at the Department of Mathematics and Mechanics at the University of Leningrad. The theory of structural stability has been developed intensively over the last 25 years. This theory is now a vast domain of mathematics, having close relations to the classical qualitative theory of differential equations, to differential topology, and to the analysis on manifolds. Evidently it is impossible to present a complete and detailed account of all fundamental results of the theory during a one year course. So the purpose of the course of lectures (and also the purpose of this book) was more modest. The author was going to give an introduction to the language of the theory of structural stability, to formulate its principal results, and to introduce the students (and also the readers of the book) to some of the main methods of this theory. One can select two principal aspects of modern theory of structural stability (of course there are some conventions attached to this state­ ment). The first one, let us call it the "geometric" aspect, deals mainly with the description of the picture of trajectories of a system; and the second, let us say the "analytic" one, has in its centre the method for solving functional equations to find invariant manifolds, conjugating homeomorphisms, and so forth.

Keywords

analysis on manifolds differential equation functional equation global analysis manifold stability

Authors and affiliations

  • Sergei Yu. Pilyugin
    • 1
  1. 1.Department of Mathematics and MechanicsState University Petrodvorets, Bibliotechnaya pI. 2St. PetersburgRussia

Bibliographic information