Details

Autor(en) / Beteiligte

• Arnold, Vladimir Igorevich

Titel

Catastrophe Theory [Elektronische Ressource]

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

1984

Link zum Volltext

• Volltext

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of bypassing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bibliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-controversial results from the mathematical theories of singularities and bifurcation. The author has tried to explain the essence of the fundamental results and applications to readers having minimal mathematical background but the reader is assumed to have an inquiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20