Electron. J. Diff. Equ., Vol. 2013 (2013), No. 274, pp. 1-22.

Cubic systems with invariant affine straight lines of total parallel multiplicity seven

Alexandru Suba, Vadim Repesco, Vitalie Putuntica

Abstract:
In this article, we study the planar cubic differential systems with invariant affine straight lines of total parallel multiplicity seven. We classify these system according to their geometric properties encoded in the configurations of invariant straight lines. We show that there are only 17 different topological phase portraits in the Poincar\'e disc associated to this family of cubic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and rescaling of the time variable.

Submitted May 15, 2013. Published December 17, 2013.
Math Subject Classifications: 34C05.
Key Words: Cubic differential system; invariant straight line; phase portrait.

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Alexandru Suba
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str., Chisinau, MD-2028, Moldova
email:suba@math.md
Vadim Repesco
Tiraspol State University
5 Gh. Iablocichin str.
Chisinau, MD-2069, Moldova
email: repescov@gmail.com
Vitalie Putuntica
Tiraspol State University
5 Gh. Iablocichin str.
Chisinau, MD-2069, Moldova
email: vitputuntica@mail.ru

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