Singularities of Differentiable Maps, Volume 1: Classification of Critical Points, Caustics and Wave Fronts

by Vladimir I. Arnold, S.M. Gusein-Zade, Alexander N. Varchenko

​Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science.  The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities.  The second volume describes the topological and algebro-geometrical aspects of the monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.

The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level.  With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.

Kindle Edition

First published October 1, 2011

About the author

Vladimir Igorevich Arnold (alternative spelling Arnol'd, Russian: Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010)[1] was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result—the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.