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

 

Quadratic Morse-Smale vector fields which are not structurally stable


Authors: Carmen Chicone and Douglas S. Shafer
Journal: Proc. Amer. Math. Soc. 85 (1982), 125-134
MSC: Primary 58F09; Secondary 34D30
MathSciNet review: 647911
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Abstract: An example is given of a quadratic system in the plane which is Morse-Smale but not structurally stable. Also, it is proved that no such example exists for a quadratic system which is a gradient.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0647911-9
PII: S 0002-9939(1982)0647911-9
Keywords: Morse-Smale, structural stability, quadratic system
Article copyright: © Copyright 1982 American Mathematical Society