Catastrophe Theory by Vladimir I. Arnold
A concise, rigorous introduction to the mathematics of singularities and bifurcations in smooth systems, developing the classification of elementary catastrophes (fold, cusp, swallowtail, butterfly, and the elliptic, hyperbolic, and parabolic umbilics), the geometry of caustics and wave fronts, and the tools of normal forms, versal deformations, and structural stability. It links these ideas to gradient dynamics and Morse theory, provides illustrative examples from mechanics and optics, and distinguishes solid applications from overextended claims.
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- Russian
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- Alternate Titles
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- Teoriya katastrof
- Теория катастроф
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