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A proof of the Jacobian conjecture on global asymptotic stability
Chen, PN; He, JX; Qin, HS
2001
Source PublicationACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN1000-9574
Volume17Issue:1Pages:119-132
AbstractLet f is an element of C-1 (R-2, R-2), f(0) = 0. The Jacobian Conjecture states that if for any x is an element of R-2, the eigenvalues of the Jacobian matrix Df(x) have negative real parts, then the zero solution of the differential equation x (over dot) = f(x) is globally asymptotically stable. In this paper we prove that the conjecture is true.
Keywordplane differential equation global stability global injectivity
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000166696200010
PublisherSPRINGER-VERLAG SINGAPORE PTE LTD
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/16720
Collection中国科学院数学与系统科学研究院
Affiliation1.China Inst Metrol, Div Mat, Hangzhou 310034, Peoples R China
2.Xiamen Univ, Dept Syst Sci, Xiamen 361005, Peoples R China
3.Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Chen, PN,He, JX,Qin, HS. A proof of the Jacobian conjecture on global asymptotic stability[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2001,17(1):119-132.
APA Chen, PN,He, JX,&Qin, HS.(2001).A proof of the Jacobian conjecture on global asymptotic stability.ACTA MATHEMATICA SINICA-ENGLISH SERIES,17(1),119-132.
MLA Chen, PN,et al."A proof of the Jacobian conjecture on global asymptotic stability".ACTA MATHEMATICA SINICA-ENGLISH SERIES 17.1(2001):119-132.
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