Algebraic and geometric invariants in qualitative study of polynomial differential systems
| Programmee: | Institutional Projects (Supreme Council for Science and Technological Development) |
| Code: | 15.817.02.03F |
| Execution period: | 2015 – 2019 |
| Institutions: | Institute of Mathematics and Computer Science |
| Project Leader: | Vulpe Nicolae |
| Participants: | Popa Mihail, Suba Alexandru, Dovbush Peter, Dryuma Valery, Baltag Valeriu, Calin Iurie, Orlov Victor, Bujac Cristina, Ciubotaru Stanislav, Vacaraș Olga |
Summary
The objectives: the solution of some actual problems in differential equations, the dissemination and popularization of obtained results as well as the specification of the ways and possibilities for applications and implementation of the results.
The role and significance of the project consist: (i) in the ensuring of continuity and succession in the research work; (ii) in the support and progress of the scientific schools existing in our country; (iii) in the implication of the youth in research work; (iv) in the extension of the sphere of application of scientific results. In particular, the application of theoretical results of this domain in some problems of biology, medicine, ecology, energetic, is supposed.
The necessary conditions for realization of the planned tasks are partially ensured by the existence of a strong collective of specialists of high qualification (1 corresponding member of ASM, 4 doctors habilitat and 4 doctors in sciences). Continuing the traditions of the scientific school founded by well-known mathematician from Moldova academician C. Sibirschi, this collective can realize the planned tasks on the high level of the last performances in domains.
The expected results:
- Some new methods for the applications of the invariant theory in the study of algebraic and geometric properties of dynamica systems with important aplications in diverse domains of natural sciences will be elaborated. In particular invariant polynomials will be used to classify the configurations of the invariant curves of the first and second degree for cubic and quadratic systems.
- Lie algebra methods as well as graded comutative algebra methods with the aplications in the study of bi- and multi-dimensional polynomial differe-ntial systems wil be developed.
- New problems related to the applications of the generated function theory and Hilbert series to graded Sibirschi algebras of polynomial systems will be considered.
- Polynomial differential systems possessing resonance singularities will be Investigated.
- Necessary and sufficient GL(2,R)-invariant conditions for distinguishing of a center from a focus will be constructed for some classes of planar polynomial systems.
- Multidimensional transformations of the godograph type will be applied for integration of non-linear differential equations and systems.
- Some gemetric methods of the function theory will be applied to the study of the boundary behavior of the functions of several complex variables.
