CUBIC SYSTEMS WITH SEVEN INVARIANT STRAIGHT LINES ALONG ONE DIRECTION, WHEN SOME STRAIGHT LINES ARE COMPLEX CONJUGATE
pdf (Русский)

Keywords

cubic differential system, invariant straight line, Darboux integrability.

How to Cite

REPEȘCO, V. (2020). CUBIC SYSTEMS WITH SEVEN INVARIANT STRAIGHT LINES ALONG ONE DIRECTION, WHEN SOME STRAIGHT LINES ARE COMPLEX CONJUGATE. Acta Et Commentationes Exact and Natural Sciences, 8(2), 70-75. https://doi.org/10.36120/2587-3644.v8i2.70-75

Abstract

Consider the generic cubic differential system x = P(x, y), y = Q(x, y), where P,Q ∈ R[x, y], max degP, degQ = 3, 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 8 canonical forms for cubic differential systems which possess invariant straight lines along one direction of total multiplicity seven including the straight line at the infinity and at least one planar invariant straight line is complex. 

https://doi.org/10.36120/2587-3644.v8i2.70-75
pdf (Русский)
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.