A proof of the Jacobian conjecture on global asymptotic stability

Authors
Chen, PN He, JX Qin, HS
Citation
Pn. Chen et al., A proof of the Jacobian conjecture on global asymptotic stability, ACTA MATH S, 17(1), 2001, pp. 119-132
Citations number
18
Categorie Soggetti
Mathematics
Journal title
ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN journal
10009574 → ACNP
Volume
17
Issue
1
Year of publication
2001
Pages
119 - 132
Database
ISI
SICI code
1000-9574(200101)17:1<119:APOTJC>2.0.ZU;2-K
Abstract
Let f is an element of C-1 (R-2, R-2), f(0) = 0. The Jacobian Conjecture st ates that if for any x is an element of R-2, the eigenvalues of the Jacobia n matrix Df(x) have negative real parts, then the zero solution of the diff erential equation x (over dot) = f(x) is globally asymptotically stable. In this paper we prove that the conjecture is true.