Singularity theory I. Transl. from the Russian by A. Iacob. 2nd printing of the 1st ed. 1993. (English) Zbl 0901.58001

Berlin: Springer. 245 p. (1998).
The first edition of this book appeared as “Dynamical systems VI” in the “Encycl. Math. Sci. 6 (1993; Zbl 0786.00006)”. The Russian original appeared as “Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 6 (1988; Zbl 0655.00013)”.
The book contains four chapters: “Critical points of functions”, “Monodromy groups of critical points”, “Basic properties of maps”, and “The global theory of singularities”. It has illustrative examples, a very good bibliography, and it should be in the personal library of every mathematician or physicist interested in modern mathematical analysis.


58-06 Proceedings, conferences, collections, etc. pertaining to global analysis
00B15 Collections of articles of miscellaneous specific interest
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces