{"id":54,"date":"2026-07-06T11:43:18","date_gmt":"2026-07-06T10:43:18","guid":{"rendered":"https:\/\/idcmi.usm.md\/?page_id=54"},"modified":"2026-07-15T14:23:02","modified_gmt":"2026-07-15T13:23:02","slug":"laboratorul-ecuatii-diferentiale","status":"publish","type":"page","link":"https:\/\/idcmi.usm.md\/?page_id=54","title":{"rendered":"Laboratorul Ecua\u021bii Diferen\u021biale"},"content":{"rendered":"<h3>Direc\u0163ii de cercetare<\/h3>\n<p>&nbsp;<\/p>\n<ul>\n<li>Teoria calitativ\u00e3 a ecua\u0163iilor diferen\u0163iale \u015fi teoria invarian\u0163ilor algebrici;<\/li>\n<li>Aplicarea analizei de grup \u015fi algebrelor Lie \u00een studiul ecua\u0163iilor diferen\u0163iale;<\/li>\n<li>Analiza func\u0163ional\u00e3 \u015fi a func\u0163iilor complexe normale.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Proiecte \u00een derulare<\/h3>\n<p>Proiectul Institu\u0163ional\u00a0<a href=\"http:\/\/www.math.md\/projects\/15.817.02.03F\/\" target=\"_blank\" rel=\"noopener\">&#8220;Invarian\u0163i algebrici \u015fi geometrici \u00een studiul calitativ al sistemelor diferen\u0163iale polinomiale&#8221;<\/a>, 2015-2019, conduc\u0103tor \u2013 Vulpe Nicolae.<\/p>\n<h3>Rezultate importante<\/h3>\n<ul>\n<li>Au fost depistate toate configura\u0163iile globale de singularit\u0103\u0163i (finite \u015fi infinite) geometric distincte, posibile pentru familia de sisteme diferen\u0163iale p\u0103tratice, \u00een cazul existen\u0163ei a trei singularit\u0103\u0163i finite reale distincte. \u00cen total au fost depistate 147 de configura\u0163ii globale geometric distincte \u015fi au fost determinate criteriile afin invariante de realizare a fiecareia dintre ele. (Vulpe N., Bujac C.) (2013)<\/li>\n<li>A fost ob\u0163inut\u0103 o estima\u0163ie numeric\u0103 finit\u0103 pentru m\u0103rimile Lyapunov algebric independente, ce intervin \u00een rezolvarea problemei centrului \u015fi focarului pentru orice sistem de ecua\u0163ii diferen\u0163iale polinomiale. Acest lucru a permis s\u0103 fie formulata pentru prima dat\u0103 o ipotez\u0103 argumentat\u0103 c\u0103 aceste numere g\u0103site constitue o margine superioar\u0103 a num\u0103rului de m\u0103rimi Lyapunov ce ar rezolva completamente problema generalizat\u0103 a centrului \u015fi focarului pentru fiecare sistem diferen\u0163ial polinomial \u00een parte. (Popa M., Pricop V.) (2013)<\/li>\n<li>Au fost stabilite propriet\u0103\u0163ile principale ale sistemelor cubice de ecua\u0163ii diferen\u0163iale cu drepte invariante. Pe baza lor au fost determinate toate configura\u0163iile din \u015fapte drepte realizabile \u00een clasa sistemelor cubice ceia ce a permis s\u0103 fie efectuat\u0103 clasificarea tuturor sistemelor diferen\u0163iale cubice ce posed\u0103 drepte invariante de multiplicitate paralel\u0103 total\u0103 egal\u0103 cu \u015fapte. S-a demonstrat c\u0103 pentru sistemul cubic multiplicitatea geometric\u0103 maximal\u0103 a unei drepte afine invariante sau a dreptei de la infinit nu este mai mare ca \u015fapte.(A. \u015eub\u0103) (2013)<\/li>\n<li>Au fost stabilite propriet\u0103\u0163ile de baz\u0103 ale sistemelor cubice de ecua\u0163ii diferen\u0163iale cu drepte invariante \u015fi pe baza lor, \u00een cazul infinitului degenerat, au fost construite configura\u0163iile posile ale acestor drepte.(O.Vacara\u015f) (2013)<\/li>\n<li>Pentru sistemul bidimensional de ecua\u0163ii diferen\u0163iale cu neliniarit\u0103\u0163i de gradul patru au fost construite primele \u015fapte constante Liapunov nenule. (Calin Iu., Ciubotaru S.) (2013)<\/li>\n<li>Pentru unele clase de sisteme p\u0103tratice \u015fi cubice de ecua\u0163ii diferen\u0163iale cu punct singular de tip centru \u00een originea de coordonate a fost construit factorul integrant invers invariant. (Calin Iu., Baltag V.) (2013)<\/li>\n<li>Au fost ob\u0163inute estima\u0163iile pentru func\u0163iile olomorfe ce elibereaz\u0103 dou\u0103 valori \u015fi cercetat principiul Lindelof \u00een \u0421^n.(P. Dovbu\u015f) (2013)<\/li>\n<li>Au fost cercetate propriet\u0103\u0163ile sistemulor 3 si 4-idimensionale de ecua\u0163ii diferen\u0163iale de ordinul \u00eent\u00e2i omogene p\u0103tratice conexe cu ecua\u0163ii bidimensional de ordinul doi. (Driuma V.) (2013)<\/li>\n<li>A fost determinat sistemul de ecua\u0163ii algebrice, r\u0103spunz\u0103tor de factor integrant Lie pentru sistemele diferen\u0163iale cu omogenit\u0103\u0163ile p\u0103tratice de tip Darboux. (Orlov V.) (2013)<\/li>\n<li>A fost efectuat\u0103 stratificarea afin invariant\u0103 a spa\u0163iului de dimensiunea 12 al coeficien\u0163ilor familiei de sisteme p\u0103tratice \u00een raport cu toate configura\u0163iile posibile de singularit\u0103\u0163i finite. Totodat\u0103 pentru aceast\u0103 familie de sisteme a fost depistat\u0103 formula de determinare a gradului de libertate a unui sistem p\u0103tratic la fixarea configura\u0163iei de singularit\u0103\u0163i finite \u015fi infinite (reale \u015fi\/sau imaginare, simple \u015fi\/sau multiple), \u015fi anume: Suma gradului de libertate \u015fi a numarului de singularit\u0103\u0163i finite distincte este egala cu patru. (N. Vulpe)<\/li>\n<li>A fost construita seria Hilbert a algebrei comitantilor unimodulari pentru sistemul de ecuatii diferentiale cu nelinearitati de ordinul cinci si a fost aratata relatia dintre seriile Hilbert ale acestor algebre pentru ecuatiile diferentiale cu nelinearitati impare (M. Popa, V. Pricop).<\/li>\n<li>Au fost stabilite proprietatile de baza ale sistemelor cubice de ecuatii diferentiale cu drepte invariante si pe baza lor, \u00een cazul infinitului degenerat, au fost construite configuratiile posile ale acestor drepte (A. Suba).<\/li>\n<p>Sunt cercetate propriet\u0103\u0163ile extensiunilor riemanienne cu conexiunea afin\u0103 constant\u0103, ce sunt determinate de sistemele de ecua\u0163ii diferen\u0163iale neliniare de ordinul \u00eent\u00eei.<\/p>\n<li>Este elaborat exemplul spa\u0163iului Ricci-plat patrudimensional cu conexiunea afin\u0103, ce depinde de solu\u0163iile ecua\u0163iei Kadomtsev-Petiashvili. (V. Driuma)<\/li>\n<li>Sunt stabilite condi\u0163iile necesare \u015fi suficiente pentru normalitatea func\u0163iilor olomorfe pe variet\u0103\u0163i complexe Banah. (P.Dovbu\u015f)<\/li>\n<li>Pentru sistemele polinomiale bidimensionale de ecua\u0163ii diferen\u0163iale de tip Darboux cu nelinia-rit\u0103\u0163i de orice grad r au fost construite integrale particulare invariante \u015fi integralele prime.(V. Baltag, Iu. Calin)<\/li>\n<\/ul>\n<h3>Publica\u0163ii electronice:<\/h3>\n<ul>\n<li>Dovbush P. V. On a Normality Criterion of S. Mandelbrojt, 2013.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1302.1695\" target=\"_blank\" rel=\"noopener\">http:\/\/arxiv.org\/abs\/1302.1695<\/a><\/li>\n<li>Popa M., Pricop V. Applications of algebraic methods in solving the center-focus problem.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1310.4343\" target=\"_blank\" rel=\"noopener\">http:\/\/arxiv.org\/abs\/1310.4343<\/a><\/li>\n<\/ul>\n<h3>Lucr\u0103ri de referin\u0163\u0103<\/h3>\n<ol>\n<li>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)<\/li>\n<li>Dovbush P. V. The Lindel\u00f6f principle in C^n. Central European Journal of Mathematics, July, 2013 Volume 11, Issue 10, pp 1763-1773. (IF: 0.34, MathSciNet)<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>Orlov V. Lie theorem on integrating factor for polynomial differential systems. ROMAI J., v.9, no.1 (2013), pp. 123\u2013132.<\/li>\n<li>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 &#8211; 354.<\/li>\n<li>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 \u2013 62. ISSN: 1024-7696<\/li>\n<li>Popa M., Pricop V. Applications of algebraic methods in solving the center-focus problem. Bul. Acad. \u015etiin\u0163e Repub. Mold. Mat. 2013, no. 1(71), pp. 45\u201371.<\/li>\n<li>Artes J. C., Llibre J., Schlomiuk D., Vulpe N. Configurations of singularities for quadratic differential systems with total finite multiplicity m_f\u22641. CRM Preprint no. 3324, Montreal, February 2013, 1\u201451.<\/li>\n<li>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\u201449.<\/li>\n<li>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, n\u00fam. 15, 2013, Universitat Aut\u00f3noma de Barcelona, 1\u201463.<\/li>\n<li>Artes J. C., Llibre J., Schlomiuk D., Vulpe N. Configurations of singularities for quadratic differential systems with three real finite distinct singularities. Preprint, n\u00fam. 16, 2013, Universitat Aut\u00f3noma de Barcelona, 1\u201443.<\/li>\n<li>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\u201430.<\/li>\n<li>Bujac C., Vulpe N. Cubic systems with invariant lines of total multiplicity eight and with four distinct infinite singularities. Preprint, n\u00fam. 10, 2013, Universitat Aut\u00f3noma de Barcelona, 1\u201451.<\/li>\n<li>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\u20136582.<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>Dovbush P. V. On the Lindelof-Gehring-Lohwater theorem. Complex Variables and Elliptic Equations, Vol. 56, Issue 5 , 2011, p. 417-421.<\/li>\n<li>Driuma V. On the equations defining the Ricci-flows of manifolds. ArXiv: 1111.3876. 2011, p. 1-7.<\/li>\n<li>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).<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>Driuma V. On spaces related to the Navier-Stokes equations.\u00a0Buletinul Academiei de Stiinte al Rep. Moldova, Matematica, 2010, no.3(64), p. 107-110.<\/li>\n<li>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\u20143558.<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>Popa M. N. Lie algebra and differential systems. Tiraspol State University (Chisinau), Acad. of Sciences of Moldova, Chisinau, 2008 163 p. (Romanian).<\/li>\n<li>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.<\/li>\n<li>Dovbush P. Bloch functions on complex Banach manifolds. Mathematical Proceedings of the Royal Irish Academy, v. 108, Issue 1, 2008, p. 27-32.<\/li>\n<li>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.<\/li>\n<li>Driuma V. Eight- dimensional the Ricci flat space related with the KP-equation. ArXiv: 0810.0346 v1 nlin.SI, Jul 2008, p. 1-5.<\/li>\n<li>Driuma V. Towards the theory of Benney equation. ArXiv: 0805.0010 v1 nlin.SI, May 2008, p. 1-11.<\/li>\n<li>Driuma V. On geometry of the Rossler system of equations. ArXiv: nlin\/0807.1063 , v 1, Jul 2008, p. 1-10.<\/li>\n<li>Driuma V. Riemann geometry in theory of the first order systems of equations. ArXiv: 0807.0178 v1 nlin.SI, Jul 2008 p. 1-17.<\/li>\n<li>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\u2014362.<\/li>\n<li>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.<\/li>\n<li>Vulpe N., Schlomiuk D. Planar quadratic differential systems with invariant straight lines of total multiplicity four. Nonlinear Analysis. Theory, Methods &amp; Applications, 2008, 68, No. 4, p. 681\u2014715.<\/li>\n<li>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\u20142076.<\/li>\n<li>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.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Direc\u0163ii de cercetare &nbsp; Teoria calitativ\u00e3 a ecua\u0163iilor diferen\u0163iale \u015fi teoria invarian\u0163ilor algebrici; Aplicarea analizei de grup \u015fi algebrelor Lie \u00een studiul ecua\u0163iilor diferen\u0163iale; Analiza func\u0163ional\u00e3 \u015fi a func\u0163iilor complexe normale. &nbsp; Proiecte \u00een derulare Proiectul Institu\u0163ional\u00a0&#8220;Invarian\u0163i algebrici \u015fi geometrici \u00een studiul calitativ al sistemelor diferen\u0163iale polinomiale&#8221;, 2015-2019, conduc\u0103tor \u2013 Vulpe Nicolae. Rezultate importante Au [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-54","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages\/54","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=54"}],"version-history":[{"count":2,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages\/54\/revisions"}],"predecessor-version":[{"id":144,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages\/54\/revisions\/144"}],"wp:attachment":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=54"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}