Book Review
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MathSciNet review:
1568120
Full text of review:
PDF
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Book Information:
Author:
Michail Zhitomirskii
Title:
Typical singularities of differential 1-forms and Pfaffian equations
Additional book information:
American Mathematical Society, Providence, RI, 1992, xi\,+176 pp., US$116.00. ISBN 0-8218-4567-5.
V. I. Arnol′d, Contact geometry and wave propagation, Monographies de L’Enseignement Mathématique [Monographs of L’Enseignement Mathématique], vol. 34, L’Enseignement Mathématique, Geneva, 1989. Série des Conférences de l’Union Mathématique Internationale [Lecture Series of the International Mathematics Union], 9. MR 1033735
Vladimir I. Arnold, Valery V. Kozlov, and Anatoly I. Neishtadt, Mathematical aspects of classical and celestial mechanics, 3rd ed., Encyclopaedia of Mathematical Sciences, vol. 3, Springer-Verlag, Berlin, 2006. [Dynamical systems. III]; Translated from the Russian original by E. Khukhro. MR 2269239
V. I. Arnol′d and A. B. Givental′, Symplectic geometry, Current problems in mathematics. Fundamental directions, Vol. 4, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1985, pp. 5–139, 291 (Russian). MR 842908
V. I. Arnol′d, A. N. Varchenko, and S. M. Guseĭn-Zade, Osobennosti differentsiruemykh otobrazheniĭ, “Nauka”, Moscow, 1982 (Russian). Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov. [Classification of critical points, caustics and wave fronts]. MR 685918
G. R. Belickiĭ, Functional equations, and local conjugacy of mappings of class $C^{\infty }$, Mat. Sb. (N.S.) 91(133) (1973), 565–579, 630 (Russian). MR 0358852
V. V. Lyčagin, Local classification of first order nonlinear partial differential equations, Uspehi Mat. Nauk 30 (1975), no. 1(181), 101–171 (Russian). MR 0420679
Jean Martinet, Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1970), no. fasc. 1, 95–178 (French, with English summary). MR 286119
John N. Mather, Stability of $C^{\infty }$ mappings. III. Finitely determined mapgerms, Inst. Hautes Études Sci. Publ. Math. 35 (1968), 279–308. MR 275459
Jürgen Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286–294. MR 182927, DOI 10.1090/S0002-9947-1965-0182927-5
- [A1]
- V. I. Arnold, Contact geometry and wave propagation, Serie des Confèerences de l'Union Mathématique Internationale, no. 9, Genève, Enseign Math. (2) 34, (1989). MR 1033735 (91k:58129)
- [AKN]
- V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical aspects of classical and celestial mechanics, Encyclopaedia Math. Sci.--Dynamical Systems III, Springer-Verlag, Berlin, 1988. MR 2269239 (2008a:70001)
- [AG]
- V. I. Arnold and A. B. Givental, Symplectic geometry, Itogi Nauki i Tekhniki, Sovre mennye Problemy Matematiki Fundamental'nye Napravleniya vol. 1, VINITI, Moscow, 1985; English transl. in Encyclopaedia Math. Sci., Springer-Verlag, Berlin, 1988. MR 842908 (88b:58044)
- [AVG]
- V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of differentiable maps, Vol. 1, "Nauka", Moscow, 1982; English transl., Birkhäuser, Basel, 1985. MR 685918 (84m:58016)
- [B]
- G. R. Belitskiĭ, Functional equations and local conjugacy of mappings of class
, Mat. Sb. 91 (1973), 565-579; English transl. in Math. USSR-Sb. 20 (1974), 587-602. MR 0358852 (50:11311)
- [L]
- V. V. Lychagin, Local classification of non-linear first-order partial differential equations, Uspekhi Mat. Nauk 30 (1) (1975), 101-171; English transl. in Russian Math. Surveys 30 (1) (1975), 105-176. MR 0420679 (54:8691)
- [Mar]
- J. Martinet, Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1970), 95-178. MR 0286119 (44:3333)
- [Mat]
- J. Mather, Stability of
mappings, Part 5, Adv. Math. 4 (1970), 301-335. MR 0275461 (43:1215c)
- [M]
- J. Moser, On the volume element on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294. MR 0182927 (32:409)
Review Information:
Reviewer:
Robert Roussarie
Journal:
Bull. Amer. Math. Soc.
31 (1994), 98-102
DOI:
https://doi.org/10.1090/S0273-0979-1994-00484-7
