Geodesic
Differential conditions to verify the Jacobian Conjecture
Annales Polonici Mathematici, Tome 57 (1992) no. 3, pp. 253-263.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.
DOI : 10.4064/ap-57-3-253-263
Keywords: jacobian conditions, global injectivity, global stability

Ludwik Drużkowski 1 ; Halszka Tutaj 1

1 
@article{10_4064_ap_57_3_253_263,
     author = {Ludwik Dru\.zkowski and Halszka Tutaj},
     title = {Differential conditions to verify the {Jacobian} {Conjecture}},
     journal = {Annales Polonici Mathematici},
     pages = {253--263},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {1992},
     doi = {10.4064/ap-57-3-253-263},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-57-3-253-263/}
}
TY  - JOUR
AU  - Ludwik Drużkowski
AU  - Halszka Tutaj
TI  - Differential conditions to verify the Jacobian Conjecture
JO  - Annales Polonici Mathematici
PY  - 1992
SP  - 253
EP  - 263
VL  - 57
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-57-3-253-263/
DO  - 10.4064/ap-57-3-253-263
LA  - en
ID  - 10_4064_ap_57_3_253_263
ER  - 
%0 Journal Article
%A Ludwik Drużkowski
%A Halszka Tutaj
%T Differential conditions to verify the Jacobian Conjecture
%J Annales Polonici Mathematici
%D 1992
%P 253-263
%V 57
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-57-3-253-263/
%R 10.4064/ap-57-3-253-263
%G en
%F 10_4064_ap_57_3_253_263
Ludwik Drużkowski; Halszka Tutaj. Differential conditions to verify the Jacobian Conjecture. Annales Polonici Mathematici, Tome 57 (1992) no. 3, pp. 253-263. doi : 10.4064/ap-57-3-253-263. http://geodesic.mathdoc.fr/articles/10.4064/ap-57-3-253-263/

Cité par Sources :