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Local normal forms of functions. (English) Zbl 0336.57022


MSC:

57R45 Singularities of differentiable mappings in differential topology
58A20 Jets in global analysis

References:

[1] Arnold, V.I.: Critical points of smooth functions. In: The Vancouver International Congress of mathematicians 1974
[2] Demazure, M.: Sousgroupes alg?briques de rang maximum du group de Cremona. Annales Sc. de l’E.N.S., 4-e serie, t.3, fasc4, 507-588 (1970) · Zbl 0223.14009
[3] Gabrielov, A.M.: Bifurcations, Dynkin diagrams and the modules numbers of isolated singularities. Funct. Anal. and appl.8, N2 7-13 (1974) · Zbl 0344.32007 · doi:10.1007/BF01078593
[4] Arnold, V. I.: Normal forms of functions near degenerate critical points, Weyl groupsA k ,D k ,E k and lagrange singularities. Funct. Anal. and appl.6, N4 254-272 (1972) · Zbl 0278.57011 · doi:10.1007/BF01077644
[5] Arnold, V.I.: Classification of unimodular critical points of functions. Funct. Anal. and appl.7, N3 75-76 (1973)
[6] Dolgatchev, I.V.: Factor conical singularities of complex surfaces. Funct. Anal. and appl.8, N2 75-76 (1974) · Zbl 0304.14011 · doi:10.1007/BF02028316
[7] Koulikov, V.S.: On some singularities of surfaces. Funct. Anal. and appl.9, N1 72-73 (1975)
[8] Arnold, V.I.: Normal forms of functions in the neighbourhoods of degenerate critical points. Russian Math. surveys29, N2 11-49 (1974)
[9] Newton, I.: La m?thode des fluxions., trad. Buffon. Paris: Debure l’Ain? 1740
[10] Klein, F.: Vorlesungen ?ber die Entwicklung der Mathematik im 19 Jahrhundert. Berlin: Springer 1926 · JFM 52.0022.05
[11] Poincar?, H.: Sur les formes cubiques ternaires et quaternaires. J. Ecole Polytechn.50, 199-253 (1881)
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