V. Puţuntică, A. Şubă, “The cubic differential system with six real invariant straight lines along three directions”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, no. 2, 111

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2009, Number 2, Pages 111–130 (Mi basm230)

This article is cited in 12 scientific papers (total in 12 papers)

Research articles

The cubic differential system with six real invariant straight lines along three directions

V. Puţuntică^a, A. Şubă^b

^a Department of Mathematics, Tiraspol State University, Chişinău, Moldova
^b Department of Mathematics, State University of Moldova, Chişinău, Moldova

Full-text PDF (371 kB) Citations (12)

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Abstract: We classify all cubic systems possessing exactly six real invariant straight lines along three directions taking into account their degree of invariance. We prove that there are 6 affine different classes of such systems. For every class we carried out the qualitative investigation in the Poincaré disc.

Keywords and phrases: cubic differential system, invariant line.

Received: 05.02.2009

Bibliographic databases:

Document Type: Article

MSC: 34C05

Language: English

Citation: V. Puţuntică, A. Şubă, “The cubic differential system with six real invariant straight lines along three directions”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, no. 2, 111–130

Citation in format AMSBIB

\Bibitem{PutUba09}

\by V.~Pu\c tuntic{\u a}, A.~\c Sub{\u a}

\paper The cubic differential system with six real invariant straight lines along three directions

\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.

\yr 2009

\issue 2

\pages 111--130

\mathnet{http://mi.mathnet.ru/basm230}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2589932}

\zmath{https://zbmath.org/?q=an:1196.34039}

Linking options:

https://www.mathnet.ru/eng/basm230

https://www.mathnet.ru/eng/basm/y2009/i2/p111

This publication is cited in the following 12 articles:

Bujac C. Schlomiuk D. Vulpe N., “Cubic Differential Systems With Invariant Straight Lines of Total Multiplicity Seven and Four Real Distinct Infinite Singularities”, Electron. J. Differ. Equ., 2021
Cristina Bujac, “The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type $(3,3)$ ”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 2, 79–98
Bujac C., Vulpe N., “Cubic Differential Systems With Invariant Straight Lines of Total Multiplicity Eight Possessing One Infinite Singularity”, Qual. Theor. Dyn. Syst., 16:1 (2017), 1–30
Alexandru Şubă, Vadim Repeşco, “Cubic systems with degenerate infinity and invariant straight lines of total parallel multiplicity five”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, no. 3, 38–56
Bujac C., Llibre J., Vulpe N., “First Integrals and Phase Portraits of Planar Polynomial Differential Cubic Systems With the Maximum Number of Invariant Straight Lines”, Qual. Theor. Dyn. Syst., 15:2 (2016), 327–348
Cristina Bujac, “One subfamily of cubic systems with invariant lines of total multiplicity eight and with two distinct real infinite singularities”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 1, 48–86
Olga Vacaraş, “Cubic differential systems with two affine real non-parallel invariant straight lines of maximal multiplicity”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 3, 79–101
Bujac C., Vulpe N., “Cubic Systems With Invariant Straight Lines of Total Multiplicity Eight and With Three Distinct Infinite Singularities”, Qual. Theor. Dyn. Syst., 14:1 (2015), 109–137
Bujac C., Vulpe N., “Cubic Differential Systems With Invariant Straight Lines of Total Multiplicity Eight and Four Distinct Infinite Singularities”, J. Math. Anal. Appl., 423:2 (2015), 1025–1080
Dumitru Cozma, “Center problem for cubic systems with a bundle of two invariant straight lines and one invariant conic”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 1, 32–49
Alexandru Şubă, Vadim Repeşco, Vitalie Puţuntică, “Cubic systems with seven invariant straight lines of configuration $(3,3,1)$ ”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 81–98
Dimitru Cozma, “Center problem for a class of cubic systems with a bundle of two invariant straight lines and one invariant conic”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, no. 3, 51–66

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

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