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The Topological Classification of Complete Quadratic System with Centers of Symmetry


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 of the ASM
Institution: Institute of Mathematics and Computer Science of the ASM
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

Adobe PDF document0.39 Mb / in romanian

Thesis

CZU 517.925

Adobe PDF document 1.21 Mb / in romanian
121 pages


Keywords

quadratic differential system, singular point, center of symmetry, invariant line, phase portrait, limit cycle, global scheme of singularity, topological classiffcation

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: