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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the number of invariant lines
for polynomial systems


Authors: Zhang Xiang and Ye Yanqian
Journal: Proc. Amer. Math. Soc. 126 (1998), 2249-2265
MSC (1991): Primary 34C05
MathSciNet review: 1476400
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we will revise the mistakes in a previous paper of Zhang Xikang (Number of integral lines of polynomial systems of degree three and four, J. Nanjing Univ. Math. Biquarterly, Supplement, 1993, pp. 209-212) for the proof of the conjecture on the maximum number of invariant straight lines of cubic and quartic polynomial differential systems; and also prove the conjecture in a previous paper of the second author (Qualitative theory of polynomial differential systems, Shanghai Science-Technical Publishers, Shanghai, 1995, p. 474) for a certain special case of the $n$ degree polynomial systems. Furthermore, we will prove that cubic and quartic differential systems have invariant straight lines along at most six and nine different directions, respectively, and also show that the maximum number of the directions can be obtained.


References [Enhancements On Off] (What's this?)

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Additional Information

Zhang Xiang
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing, China 210097
Email: xzhang@pine.njnu.edu.cn

Ye Yanqian
Affiliation: Department of Mathematics, Nanjing University, Nanjing, China 210008

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04710-8
PII: S 0002-9939(98)04710-8
Keywords: Polynomial differential system, invariant line
Received by editor(s): October 30, 1996
Additional Notes: The authors were supported by the National Natural Foundation of the People’s Republic of China
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society