CANONICAL FORMS OF CUBIC DIFFERENTIAL SYSTEMS WITH REAL INVARIANT STRAIGHT LINES OF TOTAL MULTIPLICITY SEVEN ALONG ONE DIRECTION
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Keywords

cubic differential system
invariant straight line
Darboux integrability

How to Cite

REPEȘCO, V. (2018). CANONICAL FORMS OF CUBIC DIFFERENTIAL SYSTEMS WITH REAL INVARIANT STRAIGHT LINES OF TOTAL MULTIPLICITY SEVEN ALONG ONE DIRECTION. Acta Et Commentationes Exact and Natural Sciences, 6(2), 124-132. https://doi.org/10.36120/2587-3644.v6i2.124-132

Abstract

Consider the general cubic differential system x  Px, y , y  Qx, y , where
P Q x y , , R , max deg ,deg 3  P Q  , GCD P Q  , 1   . If this system has enough invariant straight
lines considered with their multiplicities, then, according to [1], we can construct a Darboux first integral.
In this paper we obtain 26 canonical forms for cubic differential systems which possess real invariant
straight lines along one direction of total multiplicity seven including the straight line at the infinity.

https://doi.org/10.36120/2587-3644.v6i2.124-132
pdf (Русский)
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