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ArticleOriginal scientific text

Title

Differential conditions to verify the Jacobian Conjecture

Authors 1, 1

Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland,

Abstract

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

ENG
jacobian conditions, global injectivity, global stability

Bibliography

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Annales Polonici Mathematici
1992/57/3
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Pages:
253-263
Main language of publication
English
Received
1991-10-30
Accepted
1992-06-15
Published
1992
Exact and natural sciences