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Articolul urmator |
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SM ISO690:2012 BUJAC, Cristina, SCHLOMIUK, Dana, VULPE, Nicolae. Configurations of invariant lines of total multiplicity 7 of cubic systems with four real distinct infinite singularities. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, pp. 26-27. ISBN 978-9975-76-247-2. |
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Conference on Applied and Industrial Mathematics Ediţia a 26-a, 2018 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, România, Romania, 20-22 septembrie 2018 | |||||||
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Pag. 26-27 | |||||||
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Consider the family of planar cubic polynomial di erential systems. Following [1] we call conguration of invariant lines of a cubic system the set of (complex) invariant straight lines (which may have real coecients), including the line at in nity, of the system, each endowed with its own multiplicity and together with all the real singular points of this system located on these invariant straight lines, each one endowed with its own multiplicity. Our main goal is to classify the family of cubic systems according to their geometric properties encoded in the con gurations of invariant straight lines of total multiplicity seven (including the line at in nity with its own multiplicity), which these systems possess. Here we consider only the subfamily of cubic systems with four real distinct in nite singularities which we denote by CSL4s1 7 . We prove that there are exactly 94 distinct con gurations of invariant straight lines for this class and present corresponding examples for the realization of each one of the detected con gurations. We remark that cubic systems with nine (the maximum number) of invariant lines for cubic systems are considered in [2], whereas cubic systems with eight invariant lines (considered with their multiplicities) are investigated in [3-7]. |
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