VolumeIII of the Collected Works of V.I. Arnold contains papers written in the years 1972 to 1979.The main theme emerging in Arnold's work of this period is the development ofsingularity theory of smooth functions and mappings.
Thevolume also contains papers by V.I. Arnold on catastrophe theory and on A.N.Kolmogorov's school, his prefaces to Russian editions of several books relatedto singularity theory, V. Arnold's lectures on bifurcations of discretedynamical systems, as well as a review by V.I. Arnold and Ya.B. Zeldovich ofV.V. Beletsky's book on celestial mechanics.
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors.
1 Modesand Quasimodes.- 2 Integrals of RapidlyOscillating Functions and Singularities of Projections of Lagrangian Manifolds.-3 Remarks on the Stationary Phase Methodand Coxeter Numbers.- 4 Normal Forms ofFunctions near Degenerate Critical Points, the Weyl Groups Ak, Dk,Ek, and LagrangianSingularities.- 5 Normal Forms ofFunctions in Neighbourhoods of Degenerate Critical Points.- 6 Critical Points of Functions andClassification of Caustics.- 7 Classification of Unimodal Critical Points of Functions.- 8 Classification of Bimodal Critical Points of Functions.- 9 Spectral Sequence for Reduction of Functions to Normal Form.- 10 Spectral Sequences for Reducing Functions to Normal Forms.- 11 Critical Points of Smooth Functions and Their Normal Forms.- 12&l3y
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