Geodesic
Sufficiency of Weierstrass Jets
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 167-176

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. Let C (r+1)(2, 1) be the set of all (r + 1)-time continuously differentiable mappings f: R 2 → R with . Two maps f and g ∈ C (r+1)(2, 1) are said to be equivalent of order r at , if at , their Taylor expansions up to and including the terms of degree ≦ r are identical. An r-jet, denoted j (r)(f), is the equivalence class of f with f being called a realization of j (r)(f). The set of all r-jets is denoted J r (2, 1). Definition. An r-jet Z ∈ Jr (2, 1) is called C 0-sufficient (in C (r+1)(2, 1)), if for any two C (r+1)(2, 1) functions f, g which realize Z, there exists a local homeomorphism h: R 2 → R 2, for which f(h(x, y)) = g(x, y) in a neighborhood of . I.e., the following diagram commutes. 
Kirschenbaum, Marc; Lu, Yung-Chen. Sufficiency of Weierstrass Jets. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 167-176. doi: 10.4153/CJM-1983-011-4
@article{10_4153_CJM_1983_011_4,
     author = {Kirschenbaum, Marc and Lu, Yung-Chen},
     title = {Sufficiency of {Weierstrass} {Jets}},
     journal = {Canadian journal of mathematics},
     pages = {167--176},
     year = {1983},
     volume = {35},
     number = {1},
     doi = {10.4153/CJM-1983-011-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-011-4/}
}
TY  - JOUR
AU  - Kirschenbaum, Marc
AU  - Lu, Yung-Chen
TI  - Sufficiency of Weierstrass Jets
JO  - Canadian journal of mathematics
PY  - 1983
SP  - 167
EP  - 176
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-011-4/
DO  - 10.4153/CJM-1983-011-4
ID  - 10_4153_CJM_1983_011_4
ER  - 
%0 Journal Article
%A Kirschenbaum, Marc
%A Lu, Yung-Chen
%T Sufficiency of Weierstrass Jets
%J Canadian journal of mathematics
%D 1983
%P 167-176
%V 35
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-011-4/
%R 10.4153/CJM-1983-011-4
%F 10_4153_CJM_1983_011_4

[1] 1. Kuo, T. C., A complete determination of c°-sufficiency in Jr(2, 1), Invent. Math. 8 (1969), 226–235. Google Scholar

[2] 2. Kuo, T. C. and Lu, Y. C., On analytic function germs of two complex variables, Topology 16 (1977), 299–310. Google Scholar

[3] 3. Lu, Y. C., Sufficiency of jets in Jr(2, 1) via decomposition, Inv. Math. 10 (1970), 119–127. Google Scholar

[4] 4. Lu, Y. C., Singularity theory and an introduction to catastrophe theory (Springer-Ver lag, N.Y., 1976). Google Scholar

[5] 5. Yu, Y. C. and Chang, S. H., On c°-sufficiency of complex jets, Can. J. Math. 4 (1973), 874–880. Google Scholar

[6] 6. Walker, R. J., Algebraic curves (Dover, N.Y., 1950). Google Scholar

Cité par Sources :