Dynamical Systems V

1. Front Matter

   Pages i-ix

   PDF

2. Bifurcation Theory

   1. Front Matter

      Pages 1-9

      PDF

   2. Bifurcations of Equilibria

      • V. I. Arnol’d

      Pages 10-38

   3. Bifurcations of Limit Cycles

      • V. I. Arnol’d

      Pages 38-79

   4. Nonlocal Bifurcations

      • V. I. Arnol’d

      Pages 79-153

   5. Relaxation Oscillations

      • V. I. Arnol’d

      Pages 154-205

3. Catastrophe Theory

   1. Front Matter

      Pages 207-208

      PDF

   2. Basic Concepts

      • V. I. Arnol’d

      Pages 207-215

   3. The Theory of Catastrophes Before Poincaré

      • V. I. Arnol’d

      Pages 215-220

   4. The Theory of Bifurcations in the Work of Poincaré

      • V. I. Arnol’d

      Pages 220-224

   5. The Theory of Bifurcations in the Work of A.A. Andronov

      • V. I. Arnol’d

      Pages 224-232

   6. Physicists’ Treatment of Catastrophes Before Catastrophe Theory

      • V. I. Arnol’d

      Pages 232-238

   7. Thom’s Conjecture

      • V. I. Arnol’d

      Pages 239-244

   8. Classifications of Singularities and Catastrophes

      • V. I. Arnol’d

      Pages 244-259

4. Back Matter

   Pages 259-274

   PDF

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

• Bifurcation Theory
• Bifurkationstheorie
• Catastrophe Theory
• Dynamical Systems
• Dynamische Systeme
• Katastrophentheorie
• bifurcation
• differential equation
• dynamical systems
• singularity

• Steklov Mathematical Institute, Moscow, Russia

  V. I. Arnol’d

Policies and ethics