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Author: Mircea Lupan Degree: doctor of physics and mathematics Speciality:  01.01.02 - Differential equations Year: 2007 Scientific adviser: Nicolae Vulpe doctor habilitat, professor, Institute of Mathematics and Computer Science Institution: Institute of Mathematics and Computer Science Scientific council: DH 30-01.01.02-27.03.08 Moldova State University

Status The thesis was presented on the 23 February, 2007 Approved by NCAA on the 19 April, 2007 Abstract – 0.39 Mb / in romanian Thesis CZU 517.925 1.21 Mb / in romanian 121 pages

Keywords

Summary

The thesis is devoted to the study of quadratic differential systems

dx/dt= a00 + a10x + a01y + a20x² + 2a11xy + a02y²=P(x; y);

dy/dt= b00 + b10x + b01y + b20x² + 2b11xy + b02y²=Q(x; y) (1)

with real coefficients.

The goal of the thesis is to determine the affine-invariant conditions for the existence of centers of symmetry on the phase plane of the systems (1), and to investigate these systems.

The main results obtained in the thesis are the following:

• Necessary and sufficient conditions for the existence of centers of symmetry on the phase plane of systems (1) are determined and these conditions are affinely-invariant;

• The construction of all possible global schemes of singularities of quadratic systems (1) with center of symmetry;

• Necessary and sufficient affinely-invariant conditions for each scheme to be realized are determined and the examples of the realization of each such scheme are constructed;

• The class of the quadratic systems (1) with center of symmetry and two parallel invariant lines (real or complex, distinct or coinciding) was examined and all (38) possible phase portraits as well as coeicient conditions for their realization are constructed.

Oficial Reviewers

• Dumitru Cozma
  doctor habilitat, associate professor (docent)
• Ion Vrabie,
  doctor în ştiinţe matematice, profesor universitar, Universitatea Alexandru Ioan Cuza, Iaşi, România

 Theses