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IMI/Structura/

Laboratorul "Ecuaţii Diferenţiale"

Direcţii de cercetare

Proiecte în derulare

Proiectul Instituţional "Probleme actuale ale algebrei şi ecuaţiilor diferenţiale: aspecte teoretice şi aplicative", 2011-2014, conducător – Popa Mihail.

Rezultate importante

Publicaţii electronice:

Lucrări de referinţă

  1. Artes 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 Math., 43 (2013), No. 6, 2013, 65p. ISSN: 0035-7596 (IF: 0.389)
  2. Dovbush P. V. The Lindelöf principle in C^n. Central European Journal of Mathematics, July, 2013 Volume 11, Issue 10, pp 1763-1773. (IF: 0.34, MathSciNet)
  3. Dovbush P. V. Estimates for Holomorphic Functions with Values in C\{0,1}, Advances in Pure Mathematics, Vol. 3, No. 6, 2013, pp. 586-589.
  4. Dryuma V. On the equations determining the Ricci-flow on manifolds, in: International Journal of Geometric Methods in Modern Physics (IJGMMP), v.10, No.4 (2013) 1320003 (9 pages), World Scientific Publishing Company, Singapore.
  5. Orlov V. Lie theorem on integrating factor for polynomial differential systems. ROMAI J., v.9, no.1 (2013), pp. 123–132.
  6. Schlomiuk D., Vulpe N. 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, 340 - 354.
  7. Artes J. C., Llibre J., Schlomiuk D., Vulpe N. Configurations of singularities for quadratic differential systems with total multiplicity m_f=1. Bul. Acad. Stiinte Repub. Mold. Mat. No. 1(71), 2013, 11 – 62. ISSN: 1024-7696
  8. Popa M., Pricop V. Applications of algebraic methods in solving the center-focus problem. Bul. Acad. Ştiinţe Repub. Mold. Mat. 2013, no. 1(71), pp. 45–71.
  9. Artes J. C., Llibre J., Schlomiuk D., Vulpe N. Configurations of singularities for quadratic differential systems with total finite multiplicity m_f≤1. CRM Preprint no. 3324, Montreal, February 2013, 1—51.
  10. Artes J. C., Llibre J., Schlomiuk D., Vulpe N. Configurations of singularities for quadratic differential systems with total finite multiplicity m_f=2. CRM Preprint no. 3325, Montreal, March 2013, 1—49.
  11. Artes J. C., Llibre J., Schlomiuk D., Vulpe N. Algorithm for determining the global geometric configurations of singularities of total finite multiplicity 2 for quadratic differential systems. Preprint, núm. 15, 2013, Universitat Autónoma de Barcelona, 1—63.
  12. Artes J. C., Llibre J., Schlomiuk D., Vulpe N. Configurations of singularities for quadratic differential systems with three real finite distinct singularities. Preprint, núm. 16, 2013, Universitat Autónoma de Barcelona, 1—43.
  13. Bujac C., Vulpe N. Cubic systems with invariant lines of total multiplicity eight and with three distinct infinite singularities. CRM Preprint no. 3331, Montreal, December 2013, 1—30.
  14. Bujac C., Vulpe N. Cubic systems with invariant lines of total multiplicity eight and with four distinct infinite singularities. Preprint, núm. 10, 2013, Universitat Autónoma de Barcelona, 1—51.
  15. Vulpe N. 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.
  16. Vulpe N., Llibre J., Mandi A. 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.
  17. Dovbush P. V. The Lindelof principle for holomorphic functions of infinitely many variables. Complex Variables and Elliptic Equations, Vol. 56, Issue 1-4 , 2011, p. 315-323.
  18. Dovbush P. V. On the Lindelof-Gehring-Lohwater theorem. Complex Variables and Elliptic Equations, Vol. 56, Issue 5 , 2011, p. 417-421.
  19. Driuma V. On the equations defining the Ricci-flows of manifolds. ArXiv: 1111.3876. 2011, p. 1-7.
  20. Popa M. N., Pricop V. M. Applications of algebras to the focus-center problem. Preprint: Institute of Mathematics and Computer Science, No.007, October 2011, 59 p. (Russian).
  21. Vulpe N., Schlomiuk D. Global classification of the planar Lotka-Volterra differential systems according to their configurations of invariant straight lines. Journal of Fixed Point Theory and Applications, Vol. 8(2010), p. 177-245.
  22. Dovbush P. V. Boundary behaviour of Bloch functions and normal functions. Complex Variables and Elliptic Equations, Vol. 55, Issue 1-3, 2010, p. 157-166.
  23. Driuma V. On spaces related to the Navier-Stokes equations. Buletinul Academiei de Stiinte al Rep. Moldova, Matematica, 2010, no.3(64), p. 107-110.
  24. Vulpe N., Artes J., Llibre J. Quadratic systems with a polynomial first integral: a complete classification in the coefficient space R^{12}. J. Differential Equations, 246(2009), p. 3535—3558.
  25. Putuntica V. and Suba A. Cubic differential systems with six real invariant straight lines along five directions. Buletinul Academiei de Stiinte al Rep. Moldova, Matematica, 2009, no.2(60), p. 111-130.
  26. Dovbush P. V. On normal and non-normal holomorphic functions on complex Banach manifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci (5), Vol. VIII (2009), p. 1-15.
  27. Popa M. N. Lie algebra and differential systems. Tiraspol State University (Chisinau), Acad. of Sciences of Moldova, Chisinau, 2008 163 p. (Romanian).
  28. Baltag V., Calin IU. The transvectants and the integrals for Darboux systems of differential equations. Buletinul Academiei de Stiinte a Republicii Moldova, Matematica, 1(56), 2008, p.4-18.
  29. Dovbush P. Bloch functions on complex Banach manifolds. Mathematical Proceedings of the Royal Irish Academy, v. 108, Issue 1, 2008, p. 27-32.
  30. Boularas D., Matei A. and Suba A. The GL(2, R)-orbits of the homogeneous polynomial differential systems, Buletinul Academiei de Stiinte al Rep. Moldova, Matematica, 2008, no.3(58), p. 44-56.
  31. Driuma V. Eight- dimensional the Ricci flat space related with the KP-equation. ArXiv: 0810.0346 v1 nlin.SI, Jul 2008, p. 1-5.
  32. Driuma V. Towards the theory of Benney equation. ArXiv: 0805.0010 v1 nlin.SI, May 2008, p. 1-11.
  33. Driuma V. On geometry of the Rossler system of equations. ArXiv: nlin/0807.1063 , v 1, Jul 2008, p. 1-10.
  34. Driuma V. Riemann geometry in theory of the first order systems of equations. ArXiv: 0807.0178 v1 nlin.SI, Jul 2008 p. 1-17.
  35. Vulpe N., Joan C. Artes, Jaume Llibre. Singular points for quadratic system: a complete solution of the problem in the coefficient space . International Journal of Bifurcation Theory and Chaos, Vol. 18, No.2 (2008), p. 313—362.
  36. Vulpe N. Joan C. Artes, Jaume Llibre. When singular points determine quadratic systems. Electronic Journal of Differential Equations, Vol. 2008 (2008), No. 82, p. 1-37.
  37. Vulpe N., Schlomiuk D. Planar quadratic differential systems with invariant straight lines of total multiplicity four. Nonlinear Analysis. Theory, Methods & Applications, 2008, 68, No. 4, p. 681—715.
  38. Vulpe N., Schlomiuk D. 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—2076.
  39. Vulpe N., Schlomiuk D. The full study of planar quadratic differential systems possessing a line of singularities at infinity. Journal of Dynamics and Diff. Equations, Vol. 20(2008), No.4, p. 737-775.