Stability of C ∞ mappings, III. Finitely determined map-germs
Publications Mathématiques de l'IHÉS, Tome 35 (1968), pp. 127-156 
@article{PMIHES_1968__35__127_0,
     author = {Mather, John N.},
     title = {Stability of $C^\infty $ mappings, {III.} {Finitely} determined map-germs},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {127--156},
     year = {1968},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {35},
     mrnumber = {43 #1215a},
     zbl = {0159.25001},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_1968__35__127_0/}
}
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Mather, John N. Stability of $C^\infty $ mappings, III. Finitely determined map-germs. Publications Mathématiques de l'IHÉS, Tome 35 (1968), pp. 127-156. https://www.numdam.org/item/PMIHES_1968__35__127_0/

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[3] J. Mather, Stability of C∞ mappings : I. The division theorem, Annals of Math., vol. 87, 1968, pp. 89-104 ; II. Infinitesimal stability implies stability (to appear in the Annals of Math.). | Zbl | MR

[4] J.-Cl. Tougeron, Une généralisation du théorème des fonctions implicites. Équivalence des idéaux de fonctions différentiables, C. R. Acad. Sc., Paris, t. 262, pp. 487-489 and pp. 563-565. | Zbl | MR

[5] J.-Cl. Tougeron, Idéaux de fonctions différentiables, Thèse, Université de Rennes, 1967 (to appear in the Annales de l'Institut Fourier). | Zbl | Numdam