Abstract
The 1959 Bonn lectures of René Thom and the notes, Singularities of Differentiable Maps, by H.L. [Lev59] were a seminal first step towards a general mathematical theory of the critical points and stability of differentiable maps.1 This theory is commonly called singularity theory (not to be confused with “singularities” in general relativity — see the remark on page 176). It grew out of the earlier works of Morse, Whitney, and Thom, and initiated a flurry of activity leading to far reaching theories on stability (Mather), Lagrangian and Legendrian singularities (Arnold), and much more (e.g., Bruce and Mond [Bru-M]).
Functions, just like living beings, are characterized by their singularities. Paul Montel
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© 2001 Springer Science+Business Media New York
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Petters, A.O., Levine, H., Wambsganss, J. (2001). Critical Points and Stability. In: Singularity Theory and Gravitational Lensing. Progress in Mathematical Physics, vol 21. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0145-8_7
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DOI: https://doi.org/10.1007/978-1-4612-0145-8_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6633-4
Online ISBN: 978-1-4612-0145-8
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