Vladimir Andrunachievici Institute of Mathematics and Computer Science

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IMCS/Researchers/Laboratory "Differential Equations"/

Vulpe Nicolae

Degrees:	Dr. habil., Full Professor, Corresponding Member of the Academy of Sciences of Moldova
Function:	Principal Researcher
Date of birth:	February 22, 1949
Publications:	> 200
Foreign languages:	Russian, English, French
Phone:	72-70-59
Email:

Research interests

Qualitative theory of systems of differential equations, theory of algebraic invariants, development of algorithms and software for invariant polynomials utilization

Important publications

The family of cubic differential systems with two real and two complex distinct infinite singularities and invariant straight lines of the type (3,1,1,1).
Bujac C.; Vulpe N. Electron.J.Qual.Theory Differ.Equ. (2023), Paper No. 40, 94 pp.
Geometric configurations of singularities of planar polynomial differential systems [A global classification in the quadratic case].
Artes J.C.; Llibre J.; Schlomiuk, D.; Vulpe N. Birkhäuser/Springer, Cham, [2021], ©2021. xii+699 pp. ISBN: 978-3-030-50569-1
Geometric analysis of quadratic differential systems with invariant ellipses.
Mota M. C.; Rezende A. C.; Schlomiuk, D.; Vulpe N. Topological Methods in Nonlinear Analysis. Volume 59, No. 2A, 2022, 623—685. https://doi.org/ 10.12775/TMNA.2021.063 (IF:0,87)
Cubic differential system with invariant straight lines of total multiplicity seven and four real distinct infinite singularities.
Bujac C., Schlomiuk D., Vulpe N. In: Electron. J. Qual. Theory Differ. Equ. Vol.2021 (2021), No.83, 1-110. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
On Families QSL≥2 of Quadratic Systems with Invariant Lines of Total Multiplicity At Least 2.
Bujac, C.; Schlomiuk, D.; Vulpe N. Qualitative Theory of Dynamical Systems (2022) 21:133 pp. 1-68. https://doi.org/10.1007/s12346-022-00659-x (IF: 1,42)
Cubic differential systems with invariant straight lines of total multiplicity eight possessing one infinite singularity.
Qualitative Theory of Dynamical Systems. 2017, 16(1), 1-30 (coautor: C. Bujac).
First Integrals and Phase Portraits of Planar Polynomial Differential Cubic Systems with the Maximum Number of Invariant Straight Lines.
Qualitative Theory of Dynamical Systems. 2016, 15(2), 327-348 (coautor: C. Bujac, J. Llibre).
Family of quadratic differential systems with invariant hyperbolas: a complete classification in the space $\mathbb{R}^{12}$ }.
Electron. J. Differential Equations Vol. 2016 (2016), No. 162, 1-50 (coautori: R.D. Oliveira, A. Rezende).
Cubic differential systems with invariant straight lines of total multiplicity eight possessing one infinite singularity.
Qualitative Theory of Dynamical Systems. DOI: 10.1007/s12346-016-0188-x, pp. 1—30 (coautor: C. Bujac).
Classification of cubic differential systems with invariant straight lines of total multiplicity eight and two distinct infinite singularities.
Electronic Journal of Qualitative Theory of Differential Equations, 2015, No. 74, pp. 1–38 (coautor: C. Bujac).
From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields.
Rocky Mountain Journal of Mathematics, 2015, 45(1), pp. 29-113 (coautori: J. Artes, J. Llibre, D. Schlomiuk).
Cubic systems with invariant straight lines of total multiplicity eight and with three distinct infinite singularities.
Qualitative Theory of Dynamical Systems. 2015, 14(1), pp. 109-137 (coautor: C. Bujac).
Global configurations of singularities for quadratic differential systems with exactly three finite singularities of total multiplicity four.
Electronic Journal of Qualitative Theory of Differential Equations 2015, No. 49, pp. 1–60 (coautori: J. Artes, J. Llibre, D. Schlomiuk).
Bifurcation diagrams and quotient topological spaces under the action of the affine group of a family of planar quadratic vector fields.
International Journal of Bifurcation and Chaos. 25 (2015), No. 11, pp. 339–362 (coautori: O. Cerba-Diaconescu, D. Schlomiuk).
Cubic systems with invariant lines of total multiplicity eight and with four distinct infinite singularities.
Journal of Mathematical Analysis and Applications, 423 (2015), pp. 1025-1080 (coautor: C. Bujac).
Global configurations of singularities for quadratic differential systems with exactly two finite singularities of total multiplicity four.
Electronic Journal of Qualitative Theory of Differential Equations, 2014, No. 60, pp. 1–43 (coautori: J. Artes, J. Llibre, A. Rezende, D. Schlomiuk).
Global configurations of singularities for quadratic differential systems with total finite multiplicity three and at most two real singularities.
Qualitative Theory of Dynamical Systems, 2014, 13(2), pp. 305-351 (coautori: J. Artes, J. Llibre, D. Schlomiuk).
Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities.
Journal of Fixed Point Theory and Applications, 14 (2014), No. 2, pp. 555–-618 (coautori: J. Artes, J. Llibre, D. Schlomiuk).
Geometric configurations of singularities for quadratic differential systems with total finite multiplicity m_f=2, .
Electronic Journal of Differential Equations. Vol. 2014 (2014), No. 159, pp. 1–79 (coautori: J. Artes, J. Llibre, D. Schlomiuk).
Applications of symbolic calculations and polynomial invariants to the classification of singularities of differential systems.
CASC 2013, Lecture Notes in Computer Science 8136, Berlin, Springer, 2013, pp. 340 - 354 (coautor D. Schlomiuk).
Quadratic systems with an integrable saddle: A complete classification in the coefficient space R^12.
Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), pp. 5416–-5447 (coautori: J. Artes, J. Llibre).
Global topological classification of Lotka-Volterra quadratic differential systems.
Electronic Journal of Differential Equations. Vol. 2012 (2012), No. 64, pp. 1–69 (coautor D. Schlomiuk).
Complete geometric invariant study of two classes of quadratic systems.
Electronic Journal of Differential Equations. Vol. 2012 (2012), No. 09, pp. 1–35 (coautori: J. Artes, J. Llibre).
Characterization of the finite weak singularities of quadratic systems via invariant theory.
Nonlinear Analysis. Theory, Methods and Applications, 74 (2011), No. 4, p. 6553–-6582 (fară coautori)
Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral.
Rocky Mountain Journal of Mathematics, Vol. 41 (2011), No. 5, p. 1585–-1629 (coautori J. Llibre, A. Mahdi)
Global classification of the planar Lotka-Volterra differential systems according to the configurations of invariant straight lines
Journal of Fixed Point Theory and Applications, 8 (2010), p. 177–-245 (coautor D. Schlomiuk).
Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space $\mathbb{R}^{12}$.
Rendiconti del Circolo Matematico di Palermo 59 (2010), p. 419–-449 (coautori: J. Artes, J. Llibre).
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.
Qualitative Theory of Dynamical Systems, 9 (2010), No. 1-2, p. 251-300 (coautor D. Schlomiuk).
Quadratic systems with a polynomial first integral: a complete classification in the coefficient space $\mathbb{R}^{12}$.
J. Differential Equations, 246 (2009), p. 3535-3558 (coautori: J. Artes, J. Llibre).
Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity.
Rocky Mountain Journal of Mathematics, Vol. 38 (2008), No. 6, p. 2015-2075 (coautor D. Schlomiuk).
When singular points determine quadratic systems.
Electronic Journal of Differential Equations, Vol. 2008 (2008), No. 82, p. 1-37. (coautori: J. Artes, J.Llibre).
The full study of planar quadratic differential systems possessing a line of singularities at infinity.
Journal of Dynamics and Diff. Equations, 20 (2008), No. 4, p. 737-775 (coautor D. Schlomiuk).
The types of the singular points for quadratic system: a complete solution of the problem in the coefficient space $\mathbb{R}^{12}$.
International Journal of Bifurcation Theory and Chaos, 18, No.2 (2008), 1301--1373 (coautori: J. Artes, J. Llibre).
Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four
Buletinul A.ş.M., Matematica, No. 1(56), 2008, 27--83 (coautor D. Schlomiuk).
Planar quadratic differential systems with invariant straight lines of total multiplicity four.
Nonlinear Anal., 68 (2008), No. 4, 681-715 (coautor D. Schlomiuk).
Quadratic systems with a rational first integral of degree 2: a complete classification in the coefficient space $\mathbb{R}^{12}$.
Rendiconti Circolo Matematico di Palermo, Serie II, T. LVI (2007), 417--444 (coautori: J. Artes, J.Llibre).
Planar cubic polynomial differential systems with the maximum number of invariant straight lines.
Rocky Mountain J. Math., 36, No.4, 2006, 1301--1373 (coautor: J.Llibre).
Geometry of quadratic differential systems in the neighbourhood of the line at infinity.
J. Differential Equations, 215 (2005) 357--400 (coautor D. Schlomiuk).

Membership in Societies and Editorial Boards

Member of Editorial Board of the journal "Buletinul Academiei de Stiinte a Republicii Moldova. Matematica"
Member of the Mathematical Society of the Republic of Moldova.

Distinctions

Laureate of "Academician C. Sibirsky" Award for cycle of publications "Application of invariant polynomials in qualitative study of systems of differential equations" (2000).
Laureate of the Republican Award for Young Scientists for cycle of publications in the domain of algebraic invariants of differential systems (1978).

Activity

Deputy Chief of the scientific seminar "Qualitative Theory of Differential Equations" at the Moldova State University.
Member of the IMCS Scientific Council.
Membru al Adunării Secţiei de Ştiinţe Exacte şi Economice.

Pregătirea cadrelor ştiinţifice:
1. Dr. V. Cebanu susţinut 1987, Центроаффинные комитанты дифференциальной системы с кубическими нелинейностями и их приложения, Kiev, Universitatea de Stat T. G. Şevcenko.
2. Dr. V. Daniliuc susţinut 1988, Комитанты квадратично-кубической системы и их приложения, Odessa, Universitatea de Stat I. I. Mecinikov.
3. Dr. I. Nikolaev susţinut 1990, Центроаффинные комитанты и особые точки системы с квадратическими нелинейностями, Odessa, Universitatea de Stat I. I. Mecinikov.
4. Dr. Iu. Calin susţinut 1997, Качественное исследование некоторых классов полных квадратичных систем, Chişinău, Universitatea de Stat din Moldova.
5. Dr. A. Voldman susţinut în 1997, Comitants and singular points of quadratic differential systems, Chişinău, Universitatea de Stat din Moldova.
6. Dr. L. Gheorghiu susţinut în 1998, Repartizarea multiplicităților punctelor singulare infinite ale sistemului diferențial cubic, Chişinău, Universitatea de Stat din Moldova.
7. Dr. M. Lupan susţinut în 2007, Clasificarea topologică a sistemului pătratic complet cu centru de simetrie, Chişinău, Universitatea de Stat din Moldova.
8. Dr. C. Bujac susţinut 2016, Sisteme diferențiale cubice cu drepte invariante de multiplicitate totală opt, Chișinău, Institutul de Matematică și Informatică al Academiei de Științe a Moldovei.

Vizite la alte universităţi şi centre Ştiinţifice:

Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 10.01.2023-07.03.2023)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 01.10.2021-28.11.2021)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 31.08.2019-27.10.2019)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 12.05.2019-09.07.2019)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 26.10.2018-23.12.2018)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 20.04.2018-20.06.2018)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 29.10.2017-23.12.2017)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 05.05.2017-03.07.2017)
Universidade de São Pãulo (Brazilia – prof. R. Oliveira, 25.01.2016-25.03.2016)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 17.05.2016-16.07.2016)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 28.10.2016-23.12.2016)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 23.10.2015-23.12.2015)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 15.05.2015-13.07.2015)
Universidade de São Pãulo (Brazilia – prof. R. Oliveira, 06.02.2015-10.04.2015)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 26.10.2014-24.12.2014)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 23.05.2014-23.07.2014)
Universidade de São Pãulo (Brazilia – prof. R. Oliveira, 05.02.2014-01.04.2014)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 27.10.2013-24.12.2013)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 20.05.2013-19.07.2013)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 21.01.2013-22.03.2013)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 10.04.2012-09.06.2012)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 26.04.2011-15.06.2011)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 19.10.2011-18.12.2011)
Universitat Autònoma de Barcelona (Spain – prof. J. Artes, 6.04.2010-03.06.2010)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 20.10.2010-20.12.2010)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 01.03.2009-30.04.2009)
Institute for Advanced Study (Princeton, SUA – prof. Robert P. Langlands, 05.10.2009-05.12.2009)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 06.12.2009-16.12.2009)
Universitat Autònoma de Barcelona (Spain – prof. J. Artes, 02.05.2008-30.06.2008)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 20.10.2008-20.12.2008)
Banff International Research Station (Canada – Workshop, 23.11.2008-28.11.2008)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 10.04.2007-10.07.2007)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 18.10.2007-16.12.2007)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 05.02.2006-07.04.2006)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 24.04.2006-24.06.2006)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 17.10.2006-16.12.2006)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 06.05.2005-04.06.2005)
L’Université de Montréal (Canada – prof. D.Schlomiuk , 03.02.2005-04.05.2005)
Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 20.09.2005-20.12.2005)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 01.01.2004-04.03.2004, 04.09.2004-16.10.2004)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 20.11.2003-25.12.2003)
Universitat Autònoma de Barcelona (Spain, 01.05.2002-14.10.2002 – a câştigat concursul pentru a ţine un curs de lecţii studenţilor acestei universităţi)
Centre de Recherches Mathématiques (CRM), L’Université de Montréal (Canada, 02.06.2000-04.07.2000 – subsidat de Proramul FICU (Ref/99/PAS/09) al AUPELF-UREF, Agenţia universitară Francofonă)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 01.11.2000-15.12.2000)
The York University (Yoork, England, 15.02.1999-31.03.1999 – în cadrul programului susţinut financiar de Royal Society)
L’Université de Montréal (Canada – prof. D. Schlomiuk, 19.06.1999-02.07.1999)
Delft University of Technology (Delft, Netherlands – prof. J. Reyn, 01.02.1997-25.02.1997, a participat în calitate de referent oficial la susţinerea unei teze de doctor)

Publications in Computer Science Journal of Moldova, Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica and Quasigroups and Related Systems