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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, Number 2, Pages 81–98 (Mi basm314)  

This article is cited in 7 scientific papers (total in 7 papers)

Cubic systems with seven invariant straight lines of configuration $(3,3,1)$

Alexandru Şubăa, Vadim Repeşcob, Vitalie Puţunticăb

a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
b Tiraspol State University, Chişinău, Moldova

Abstract: We classify all cubic differential systems with exactly seven invariant straight lines (taking into account their parallel multiplicity) which form a configuration of type $(3,3,1)$. We prove that there are six different topological classes of such systems. For every class we carried out the qualitative investigation on the Poincaré disc. Some properties of cubic systems with invariant straight lines are given.

Keywords and phrases: cubic differential system, invariant straight line, phase portrait.

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Bibliographic databases:
MSC: 34C05
Received: 10.10.2012
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Citation: 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

Citation in format AMSBIB
\Bibitem{UbaRepPut12}
\by Alexandru~\c Sub{\u a}, Vadim~Repe{\c s}co, Vitalie~Pu\c tuntic{\u a}
\paper Cubic systems with seven invariant straight lines of configuration~$(3,3,1)$
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2012
\issue 2
\pages 81--98
\mathnet{http://mi.mathnet.ru/basm314}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3060804}
\zmath{https://zbmath.org/?q=an:06179498}


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

    This publication is cited in the following articles:
    1. 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  mathnet
    2. 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  crossref  mathscinet  zmath  isi  scopus
    3. 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  crossref  mathscinet  zmath  isi  scopus
    4. Bujac C., Vulpe N., “Classification of Cubic Differential Systems With Invariant Straight Lines of Total Multiplicity Eight and Two Distinct Infinite Singularities”, Electron. J. Qual. Theory Differ., 2015, no. 74  mathscinet  isi
    5. 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  mathnet
    6. C. Bujac, N. Vulpe, “Cubic differential systems with invariant straight lines of total multiplicity eight possessing one infinite singularity”, Qual. Theor. Dyn. Syst., 16:1 (2017), 1–30  crossref  mathscinet  isi  scopus
    7. C. Bujac, N. Vulpe, “First integrals and phase portraits of planar polynomial differential cubic systems with invariant straight lines of total multiplicity eight”, Electron. J. Qual. Theory Differ., 2017, no. 85, 1–35  crossref  mathscinet  isi  scopus
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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