Differential conditions to verify the Jacobian Conjecture
Annales Polonici Mathematici, Tome 57 (1992) no. 3, pp. 253-263
Cet article a éte moissonné depuis 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.
Keywords:
jacobian conditions, global injectivity, global stability
Affiliations des auteurs :
Ludwik Drużkowski 1 ; Halszka Tutaj 1
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author = {Ludwik Dru\.zkowski and Halszka Tutaj},
title = {Differential conditions to verify the {Jacobian} {Conjecture}},
journal = {Annales Polonici Mathematici},
pages = {253--263},
year = {1992},
volume = {57},
number = {3},
doi = {10.4064/ap-57-3-253-263},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-57-3-253-263/}
}
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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
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