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Nonlinear Stability and Bifurcation Theory

An Introduction for Engineers and Applied Scientists

  • Hans Troger
  • Alois Steindl

Table of contents

  1. Front Matter
    Pages i-xi
  2. Hans Troger, Alois Steindl
    Pages 1-22
  3. Hans Troger, Alois Steindl
    Pages 23-45
  4. Hans Troger, Alois Steindl
    Pages 46-68
  5. Hans Troger, Alois Steindl
    Pages 69-142
  6. Hans Troger, Alois Steindl
    Pages 143-178
  7. Hans Troger, Alois Steindl
    Pages 179-286
  8. Back Matter
    Pages 287-408

About this book

Introduction

Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin­ ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir­ cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start­ ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner.

Keywords

chaos deformation differential equation dynamical systems geometry mechanics model modeling operator stability transformation

Authors and affiliations

  • Hans Troger
    • 1
  • Alois Steindl
    • 1
  1. 1.Technical University ViennaViennaAustria

Bibliographic information