Author | Arnold, Vladimir Igorevich. author |
---|---|

Title | Catastrophe Theory [electronic resource] / by Vladimir Igorevich Arnold |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1984 |

Connect to | http://dx.doi.org/10.1007/978-3-642-96799-3 |

Descript | IX, 79p. 65 illus. online resource |

SUMMARY

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 byยญ passing 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 biยญ bliography 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-conยญ troversial results from the mathematical theories of singulariยญ ties and bifurcation. The author has tried to explain the essence of the fundamenยญ tal results and applications to readers having minimal matheยญ matical background but the reader is assumed to have an inยญ quiring 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

CONTENT

1. Singularities, Bifurcations, and Catastrophe Theories -- 2. Whitneyโ{128}{153}s Singularity Theory -- 3. Applications of Whitneyโ{128}{153}s Theory -- 4. A Catastrophe Machine -- 5. Bifurcations of Equilibrium States -- 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations -- 7. Singularities of Stability Boundaries and the Principle of the Fragility of Good Things -- 8. Caustics, Wave Fronts and Their Metamorphoses -- 9. Large Scale Distribution of Matter in the Universe -- 10. Singularities in Optimization Problems, the Maxima Function -- 11. Singularities of Accessibility Boundaries -- 12. Smooth Surfaces and Their Projections -- 13. Problems of By-Passing Obstacles -- 14. Symplectic and Contact Geometries -- 15. The Mystics of the Catastrophe Theory -- References

Mathematics
Numerical analysis
Mathematics
Numerical Analysis