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@article{BASM_2013_1_a0, author = {Dana Schlomiuk}, title = {New developments based on the mathematical legacy of {C.\,S.~Sibirschi}}, journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica}, pages = {3--10}, publisher = {mathdoc}, number = {1}, year = {2013}, language = {en}, url = {https://geodesic-test.mathdoc.fr/item/BASM_2013_1_a0/} }
TY - JOUR AU - Dana Schlomiuk TI - New developments based on the mathematical legacy of C.\,S.~Sibirschi JO - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica PY - 2013 SP - 3 EP - 10 IS - 1 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/item/BASM_2013_1_a0/ LA - en ID - BASM_2013_1_a0 ER -
Dana Schlomiuk. New developments based on the mathematical legacy of C.\,S.~Sibirschi. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2013), pp. 3-10. https://geodesic-test.mathdoc.fr/item/BASM_2013_1_a0/
[1] Artés J. C., Llibre J., “Quadratic vector fields with a weak focus of third order”, Publ. Mat., 41 (1997), 7–39 | DOI | MR | Zbl
[2] Artés J. C., Llibre J., Schlomiuk D., “The geometry of quadratic dufferential systems with a weak focus of second order”, International J. of Bifurcation and Chaos, 16 (2006), 3127–3194 | DOI | MR | Zbl
[3] Artés J. C., Llibre J., Schlomiuk D., Vulpe N., “From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields”, Rocky Mountain J. of Mathematics (to appear)
[4] Artés J. C., Llibre J., Schlomiuk D., Vulpe N., “Geometric configurations of singularities for quadratic differential systems with total finite multiplicity lower than 2”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2013, no. 1(71), 72–124 | Zbl
[5] Artés J. C., Llibre J., Schlomiuk D., Vulpe N., Configurations of singularities for quadratic differential systems with total finite multiplicity $m_f=2$, Preprint No 3325, CRM, Montreal, March, 2013, 49 pp.
[6] Artés J. C., Llibre J., Vulpe N., “Quadratic systems with a rational first integral of degree 2: a complete classification in the coefficient space $\mathbb R^{12}$”, Rendiconti del Circolo Matematico di Palermo, Serie II, 56 (2007), 417–444 | DOI | MR | Zbl
[7] Artés J. C., Llibre J., Vulpe N., “Singular points of quadratic systems: a complete classification in the coefficient space $\mathbb R^{12}$”, International Journal of Bifurcation Theory and Chaos, 18:2 (2008), 313–362 | DOI | MR | Zbl
[8] Artés J. C., Llibre J., Vulpe N., “Quadratic systems with a polynomial first integral: a complete classification in the coefficient space $\mathbb R^{12}$”, J. Differential Equations, 246 (2009), 3535–3558 | DOI | MR | Zbl
[9] Artés J. C., Llibre J., Vulpe N., “Quadratic systems with an integrable saddle: A complete classification in the coefficient space $\mathbb R^{12}$”, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 5416–5447 | DOI | MR | Zbl
[10] Artés J. C., Llibre J., Vulpe N., “Complete geometric invariant study of two classes of quadratic systems”, Electronic J. Differential Equations, 2012 (2012), 09, 35 pp. | MR | Zbl
[11] Baltag V., Calin Iu., “The transvectants and the integrals for Darboux systems of differential equations”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2008, no. 1(56), 4–18 | MR | Zbl
[12] Boularas Driss, Vulpe N., Sibirschi C., “Solution of a problem of the center “in the large” for a general quadratic differential system”, Differential Equations, 25:11 (1989), 1294–1299 | MR
[13] Diaconescu O. V., “Multi-dimensional Darboux type differential systems with quadratic nonlinearities”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2007, no. 1(53), 95–100 | MR | Zbl
[14] Dumortier F., Llibre J., Artés J. C., Qualitative Theory of Planar Differential Systems, Springer, 2006, 298 pp. | MR | Zbl
[15] Gherstega N., Popa M., “Lie algebras of the operators and three-dimensional polynomial systems”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2005, no. 2(48), 51–64 | MR
[16] Gherstega N., Popa M., Pricop V., “The generators of the algebras of invariants for differential system with homogeneous nonlinearities of odd degree”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2012, no. 2(69), 43–58 | Zbl
[17] Gherstega N., Orlov V., Vulpe N., “A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2009, no. 2(60), 29–54 | MR | Zbl
[18] Hilbert D., “Mathematical Ptoblems”, Lecture delivered before the International Congress of Mathematicians at Paris in 1900, Translated for, Bulletin of the AMS, 8 (1902), 437–479 | DOI | MR | Zbl
[19] Li C., “Non-existence of limit cycles around a weak focus of order three for any quadratic systems”, Chinese Ann. Math., Ser. B, 7 (1986), 174–190 | MR | Zbl
[20] Llibre J., Schlomiuk D., “The geometry of quadratic differential systems with a weak focus of third order”, Canadian J. Math., 56 (2004), 310–343 | DOI | MR | Zbl
[21] Orlov V. M., “Classification of $GL(2,\mathbb R)$-orbit's dimensions for the differential system with cubic nonlinearities”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2008, no. 3(58), 116–118 | MR | Zbl
[22] Pal J., Schlomiuk D., “Summing up the dynamics of quadratic Hamiltonian systems with a center”, Canadian J. Math., 49 (1997), 583–599 | DOI | MR | Zbl
[23] Poincaré H., “'Mémoire sur les courbes définies par les équations différentielles”, J. de Math. Pures Appl. (4), 1 (1885), 167–244; Oeuvres de Henri Poincaré, v. 1, Gauthier-Villars, Paris, 1951, 95–114
[24] Poincaré H., “Sur l'intégration algégrique des équations différentielles”, C. R. Acad. Sci. Paris, 112 (1891), 761–764 | Zbl
[25] Poincaré H., “Sur l'intégration algégrique des équations différentielles du premier ordre et du premier degré”, Rend. Circ. Mat. Palermo, 5 (1891), 169–191 | DOI
[26] Popa M., Algebraic methods for differential systems, Seria Matematică Aplicată şi Industrială, 15, Editura the Flower Power, Universitatea din Piteşti, 2004 (in Romanian) | MR | Zbl
[27] Romanovski V., Shafer D., The Center and Cyclicity problems: A Computational Algebra Approach, Birkhäuser, 2011 | MR
[28] Schlomiuk D., “Algebraic particular integrals, integrability and the problem of the center”, Trans. Amer. Math. Soc., 338 (1993), 799–841 | DOI | MR | Zbl
[29] Schlomiuk D., “The mathematical legacy of C. S. Sibirsky, basis for future work”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2003, no. 1(41), 3–6 | MR | Zbl
[30] Schlomiuk D., Vulpe N., “Planar quadratic differential systems with invariant straight lines of at least five total multiplicity”, Qualitative Theory of Dynamical Systems, 5 (2004), 135–194 | DOI | MR | Zbl
[31] Schlomiuk D., Vulpe N., “Geometry of quadratic differential systems in the neighborhood of infinity”, J. Differential Equations, 215 (2005), 357–400 | DOI | MR | Zbl
[32] Schlomiuk D., Vulpe N., “Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity”, Rocky Mountain Journal of Mathematics, 38:6 (2008), 1–60 | DOI | MR
[33] Schlomiuk D., Vulpe N., “Planar quadratic differential systems with invariant straight lines of total multiplicity four”, Nonlinear Anal., 68:4 (2008), 681–715 | DOI | MR | Zbl
[34] Schlomiuk D., Vulpe N., “Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four”, Bull. Acad. Ştiinţe. Repub. Moldova, Mat., 2008, no. 1(56), 27–83 | MR | Zbl
[35] Schlomiuk D., Vulpe N., “The full study of planar quadratic differential systems possessing a line of singularities at infinity”, Journal of Dynamics and Diff. Equations, 20:4 (2008), 737–775 | DOI | MR | Zbl
[36] Schlomiuk D., Vulpe N., “Global classification of the planar Lotka–Volterra differential systems according to their configurations of invariant straight lines”, Journal of Fixed Point Theory and Applications, 8:1 (2010), 177–245 | DOI | MR | Zbl
[37] Schlomiuk D., Vulpe N., “Global topological classification of the planar Lotka–Volterra differential systems”, Electron. J. Differential Equations, 2012 (2012), 64, 69 pp. | MR | Zbl
[38] Sibirskii K. S., Algebraic Invariants of Differential Equations and Matrices, Shtiintsa, Kishinev, 1976 (in Russian) | MR
[39] Vulpe N. N., “Affine-invariant conditions for the topological discrimination of quadratic systems with a center”, Differential Equations, 19 (1983), 273–280 | MR | Zbl
[40] Vulpe N., “Characterization of the finite weak singularities of quadratic systems via invariant theory”, Nonlinear Analysis. Theory, Methods and Applications, 74:4 (2011), 6553–6582 | DOI | MR | Zbl
[41] Żoła̧dek H., “Quadratic systems with center and their perturbations”, J. Differential Equations, 109 (1994), 223–273 | DOI | MR