Dana Schlomiuk

Champs d'intérêt et thèmes d'enseignement

• Équations différentielles, Systèmes dynamiques
• Algèbre différentielle, Géométrie algébrique

Mes recherches récentes portent sur les champs de vecteurs dans le plan : intégrabilité, géométrie globale de certaines classes de systèmes différentiels polynomiaux, leurs diagrammes de bifurcations et leurs espaces de modules, applications aux problèmes classiques : 16e problème de Hilbert, problème de Poincaré, problème du centre.

Publications

Articles soumis pour publication dans des Journaux Scientifiques avec Comité de Lecture

• D. Schlomiuk and N. Vulpe, Bifurcation diagrams and moduli spaces of planar quadratic vector fields with invariant lines of total multiplicity four and having exactly three real singularities at infinity, 55 pages, soumis en 2009.

Articles publiés dans des Journaux Scientifiques avec Comité de Lecture (depuis 2002)

• J. Artés, J. Llibre and D. Schlomiuk, The geometry of quadratic polynomial differential systems with a weak focus and an invariant straight line, 41 pages, to appear in International Journal of Bifurcation and Chaos.
• D. Schlomiuk and N. Vulpe, The full study of planar quadratic differential systems possessing a line of singularities at infinity, invited article for the volume in honor of Z. Zhang, J. of Dynamics and Diff. Eq. Vol. 20, no. 4, décembre 2008, pp. 737-775.
• C. Christopher and D. Schlomiuk, On General Algebraic Mechanisms for producing Centers in Polynomial Differential Systems, J. of Fixed Point Theory, Vol. 3, No. 2, septembre 2008, pp. 331-351.
• D. Schlomiuk and N. Vulpe, Planar quadratic differential systems with invariant straight lines of total multiplicity four, Nonlinear Analysis 68 (2008), pp. 681-715.
• D. Schlomiuk and N. Vulpe, Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity, Rocky Mountain J. of Math. Vol. 38, No. 6, 2008 dans le Rocky, pp. 1-61.
• D. Schlomiuk and N. Vulpe, Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four, Buletinul Academiei de Stiinte a Republicii Moldova, Matematica, Number 1 (56), 2008, pp. 1-57.
• J. Artés, J. Llibre and D. Schlomiuk, Geometry of quadratic differential systems with a weak focus of second order, International Journal of Bifurcation and Chaos, Vol.16, No. 11 (2006), pp. 3127-3194. Cet article a été choisi comme article tutoriel par le journal.
• D. Schlomiuk and N. Vulpe, Geometry of quadratic differential systems in the neighborhood of infinity, Journal of Differential Equations 215, (2005), pp. 357-400.
• D. Schlomiuk and N. Vulpe, Planar quadratic vector fields with invariant lines of total multiplicity at least five, Qualitative Theory of Dynamical Systems, Vol. 5, (2004), pp. 135-194.
• J. Llibre and D. Schlomiuk, The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order, Canadian Journal of Mathematics, Vol. 56 (2), (2004), pp. 310-343.
• D. Schlomiuk, The mathematical legacy of C. S. Sibirsky, basis for future work, Bulletin of the Academy of Sciences of Moldova, Vol.1, 2003, pp. 3-6.
• R. Roussarie and D. Schlomiuk, On the Geometric Structure of the Class of Planar Quadratic Differential Systems, Qualitative Theory of Dyn. Syst. 3, 93-121 (2002), Article No. 33, pp. 93-121.

Livres publiés

• SCHLOMIUK D., La logica dei topos, La Goliardica Editrice, (traduction en italien du livre indiqué ci-après), 1982, 135 pages.
• SCHLOMIUK D., Logique des topos, Presses de l'Université de Montréal, 1976, 132 pages.

Livres édités

• SCHLOMIUK D., On Finiteness in Differential Equations and Diophantine Geometry CRM Monograph Series, American Mathematical Society, pp. 182, 2005.
• SCHLOMIUK D., Bifurcations and periodic orbits of Vector Fields, Kluwer Academic Publishers, NATO Advanced Study Institute Series, Series C : Mathematical and Physical Sciences, Vol. 408, 472 pages, 1993.

Chapitres de livres

• SCHLOMIUK D., Finiteness problems in differential equations and diophantine geometry in On Finiteness in Differential Equations and Diophantine Geometry CRM Monograph Series, American Mathematical Society, D. Schlomiuk Editor, 9 pp., 2005.
• SCHLOMIUK D., Aspects of planar polynomial vector fields: Global versus local, real versus complex, analytic versus algebraic and geometric, in Normal forms, Bifurcations and Finiteness Problems in Differential Equations, Yu. Ilyashenko and C. Rousseau editors, NATO Science Series, Kluwer Academic Publishers, Series II: Mathematics, Physics and Chemistry, Vol. 137, pp. 471-509, 2004.
• SCHLOMIUK D., Algebraic and geometric aspects of the theory of planar polynomial vector fields, in Bifurcations and Periodic Orbits of Vector Fields, D. Schlomiuk Editor, NATO Advanced Study Institutes Series, Series C : Mathematical and Physical Sciences, Kluwer Academic Publishers, Vol. 408, pp. 429-467, 1993.