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 SM ISO690:2012OLIVEIRA, Regilene D. S., SCHLOMIUK, Dana, TRAVAGLINI, Ana Maria. Darboux' theory of integrability for quadratic systems with invariant hyperbolas. In: Mathematics and IT: Research and Education, 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, p. 67. |
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| Mathematics and IT: Research and Education 2021 | ||||||
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Conferința "Mathematics and IT: Research and Education " Chişinău, Moldova, 1-3 iulie 2021 | ||||||
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| Pag. 67-67 | ||||||
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The goal of this work is to present the investigation in development about integrability of planar quadratic differential systems in the whole class of nondegenerate planar quadratic differential systems possessing at least one invariant hyperbola (QSH). Such class was investigated in [1] where the authors classify it according to its geometric properties encoded in the configurations of invariant hyperbolas and invariant straight lines which these systems possess. In this talk we will present results about Darboux and Liouvillian integrability for QSH. For that, we will see some important results of Darboux’ theory and investigate the existence of invariant algebraic curves, exponential factors, integrating factors and first integrals for some examples. Our main motivation in this research is to study the relationship between integrability and the geometry of the systems as expressed in their configurations of invariant algebraic curves as well as their relations with the bifurcations of the phase portraits. |
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