Cubic differential systems with resonant singularities
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StatusThe thesis was presented on the 23 July, 2021Approved by NCAA on the 4 October, 2021 Abstract – 0.85 Mb / in romanianThesisCZU 517.925
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Keywords
cubic differential system, invariant straight line, algebraic multiplicity, resonant singularity, center problem, Darboux integrabilitySummary
Thesis structure: introduction, four chapters, general conclusions and recommendations, bibliography of 143 titles, one figure, 3 tables, 127 pages of basic text. The obtained results were published in 18 scientific papers.
The purpose of the work: classification and integrability of cubic systems of differential equations with resonant singularities and with invariant straight lines of total multiplicity 4, 5, 6 and 7.
Ob jectives of the research: determination of the maximal multiplicity of an invariant straight line (of the line at infinity) for cubic differential systems with resonant singularities; classification of cubic systems with resonant singularities and with multiple invariant straight lines; studying the problem of Darboux integrability for the obtained systems.
Scientific novelty and originality consists in the investigation, for the first time, of cubic differential systems with resonant singularities and with multiple invariant straight lines, including the line at infinity. The affine classification of cubic systems with (1 ∶ −1) and (1 ∶ −2) resonant singularities and with invariant straight lines was realized. The obtained results which contribute to solve some important scientific problem: the complete solution of the center’s problem for the cubic systems with invariant straight lines (including the line at infinity) of total algebraic multiplicity five and of the integrability’s problem for the Lotka-Volterra cubic systems with (1 ∶ −2) resonant singularity and with invariant straight lines of total multiplicity 6 and 7 (including the line at infinity).
The theoretical significance: the obtained results in this thesis are new and are a significant phase of the study of the cubic systems with invariant straight lines.
Implementation of the scientific results: the results of this thesis can be used: in the further investigations of cubic systems with invariant algebraic curves, as a support for perfecting undergraduate and postgraduate optional courses, in the study of some mathematical models which describe some processes in physics, chemistry, biology, economy and others.
Oficial Reviewers
- Dumitru Cozma
doctor habilitat, associate professor (docent) - Victor Pricop
doctor, associate professor (docent)
Council's Members
- Andrei Perjan, president
doctor habilitat, professor, Moldova State University - Victor Orlov, secretary
doctor - Vasile Neagu, member
doctor habilitat, professor, Moldova State University - Mihail Popa, member
doctor habilitat, professor, Institute of Mathematics and Computer Science - Nicolae Vulpe, member
doctor habilitat, professor, Institute of Mathematics and Computer Science
Theses
