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 SM ISO690:2012BUJAC, Cristina, SCHLOMIUK, Dana, VULPE, Nicolae. The family of cubic differential systems with two real and two complex distinct infinite singularities and invariant straight lines of the type (3, 1, 1, 1). In: Electronic Journal of Qualitative Theory of Differential Equations, 2023, vol. 2023, pp. 1-94. ISSN 1417-3875. DOI: https://doi.org/10.14232/ejqtde.2023.1.40 |
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  Electronic Journal of Qualitative Theory of Differential Equations |
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| Volumul 2023 / 2023 / ISSN 1417-3875 | ||||||
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| DOI:https://doi.org/10.14232/ejqtde.2023.1.40 | ||||||
| Pag. 1-94 | ||||||
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In this article we consider the class CSL72r2c∞ of non-degenerate real planar cubic vector fields, which possess two real and two complex distinct infinite singularities and invariant straight lines of total multiplicity 7, including the line at infinity. The classification according to the configurations of invariant lines of systems possessing invariant straight lines was given in articles published from 2014 up to 2022. We continue our investigation for the family CSL72r2c∞ possessing configurations of invariant lines of type (3, 1, 1, 1) and prove that there are exactly 42 distinct configurations of this type. Moreover we construct all the orbit representatives of the systems in this class with respect to affine group of transformations and a time rescaling. |
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| Cuvinte-cheie Configurations of invariant straight lines, Cubic vector fields, infinite and finite singularities, invariant straight lines, multiplicity of invariant lines, multiplicity of singularity |
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