×

Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities. (English. Russian original) Zbl 0278.57011

Funct. Anal. Appl. 6, 254-272 (1973); translation from Funkts. Anal. Prilozh. 6, No. 4, 3-25 (1972).

MSC:

57R45 Singularities of differentiable mappings in differential topology
57R30 Foliations in differential topology; geometric theory
26E10 \(C^\infty\)-functions, quasi-analytic functions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] V. I. Arnol’d, ”Singularities of smooth maps,” UMN,23, No. 1, 3-44 (1968).
[2] J. C. Tougeron, ”Ideaux de fonctions differentiables. I,” Ann. Inst. Fourier,18, No. 1, 177-240 (1968). · Zbl 0188.45102
[3] A. M. Samoilenko, ”On equivalences of Taylor’s polynomials of smooth functions in a neighborhood of critical points of finite type,” Funktsional’. Analiz i Ego Prilozhen.,2, No. 4, 63-69 (1968).
[4] J. Milnor, Morse Theory, Princeton Univ. Press (1963).
[5] G. N. Tyurina, ”Local semiuniversal flat deformations of isolated singularities of complex spaces,” Izv. AN SSSR, Ser. Matem.,33, 1026-1058 (1969).
[6] V. I. Arnol’d, ”Lectures on bifurcation and versal families,” UMN,27, No. 5, 120-184 (1972).
[7] J. Mather, ”Structural stability of maps,” in: Singularities of Differentiated Reflections [Russian translation], Mir, Moscow (1968), pp. 216-267.
[8] V. I. Arnol’d, ”Rings of algebraic functions and the cohomology of swallow’s tails,” UMN,23, No. 4, 247-248 (1968).
[9] E. Brieskorn, ”Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe,” Invent. Math.,12, No. 1, 57-61 (1971). · Zbl 0204.56502
[10] E. Brieskorn, ”Braids,” Seminaire N. Bourbaki,24, No. 401, November, 1971. · Zbl 0716.20017
[11] A. N. Varchenko, ”On the branching of multiple integrals depending on a parameter,” Functional’. Analiz i Ego Prilozhen.,3, No. 4, 79-80 (1969).
[12] M. Artin, ”Some numerical criteria for contractibility of curves on algebraic surfaces,” Amer. J. Math.,84, 485-496 (1962). · Zbl 0105.14404
[13] E. Brieskorn, ”Die Auflösung der rationalen Singularitäten holomorphen Abbildungen,” Math. Ann.,178, 255-270 (1968). · Zbl 0159.37703
[14] G. N. Tyurina, ”Resolution of singularities of flat deformations of double rational points,” Funktional’. Analiz i Ego Prilozhen.,4, No. 1, 77-83 (1970).
[15] V. I. Arnol’d, ”On matrices depending on parameters,” UMN,26, No. 2, 101-114 (1971).
[16] E. Brieskorn, Nice Mathematical Congress, 1970.
[17] T. Springer, Budapest Symposium on Group Representations, 1971. · Zbl 0224.05002
[18] V. I. Arnol’d, ”Integrals of rapidly oscillating functions and singularities of projections of lagrangian manifolds,” Funktional’. Analiz i Ego Prilozhen.,6, No. 3, 61-62 (1972).
[19] V. I. Arnol’d, ”On characteristic classes appearing in quantization conditions,” Funktional’. Analiz i Ego Prilozhen.,1, No. 1, 1-14 (1967).
[20] J. Boardman, in: Singularities of Differentiated Reflections [Russian translation], Mir, Moscow (1968), pp. 102-153.
[21] B. Morin, Calcul Jacobien, These, Paris?Sud (1972).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.