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Author: Angela Păşcanu Degree: doctor of physics and mathematics Speciality:  01.01.02 - Differential equations Year: 2007 Scientific adviser: Alexandru Şubă doctor habilitat, professor, Tiraspol State University Institution: Scientific council:

Status The thesis was presented on the 23 March, 2007 Approved by NCAA on the 19 April, 2007 Abstract – 0.27 Mb / in romanian Thesis CZU 517.925 0.53 Mb / in romanian 80 pages

Keywords

Summary

The work is devoted to study of the GL(2; R)-orbits of polynomial differential systems. It is established that in the class of polynomial systems there are not system with the dimension of the GL(2; R)-orbits equal to one. The canonical forms for homogeneous polynomial differential systems of degree 0; 1; 2; 3 and 4 were constructed. For homogeneous polynomial systems it was proved that on the GL(2; IR)-orbits of dimension at most four the right-hand sides of the systems and of the greatest common divisor differ with a unit.

It was established the correlation between resonance, integrability and dimension of the GL(2; R)-orbits in polynomial systems with a singular point with distinct eigenvalues. In dependence of the GL(2; R)-orbits the classification for polynomial differential systems of degree four was obtained. The thesis is written in Romanian.

Oficial Reviewers

• Andrei Braicov
  doctor, associate professor (docent)
• Ilie Burdujan,
  doctor în ştiinţe matematice, profesor universitar, Iaşi, România

 Theses