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 |
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Vadim Repesco Tiraspol State University 5 Gh. Iablocichin str. Chisinau, MD-2069, Moldova email: repescov@gmail.com |
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Vitalie Putuntica Tiraspol State University 5 Gh. Iablocichin str. Chisinau, MD-2069, Moldova email: vitputuntica@mail.ru |
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