ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Phase Flows of One Family of Cubic Systems in a Poincare Circle. IV_1


A. F. Andreev

Russia, 198504, Petergof, Universitetski pr.28
S.Peterburg State University
Faculty of Mathematics and Mechanics

I. A. Andreeva

Russia, 195251, Saint-Petersburg, Politekhnicheskaya str., 29,
Saint-Petersburg state technic university,
dept. of Higher mathematics


The continuation of the investigation begun in articles with the same title No. I and II (the same journal 2007, N 4; 2008, N 1). On a real plain (x,y) a normal autonomous system of differential equations is considered, right parts of which are reciprocal forms of x and y with arbitrary constant coefficients (in one equation this form is square, and in the other equation it is cubic). In the Part I of this investigation a singular point $(0,0)$ of the system was studied, and in the Part II each of possible infinite singular points of this system are investigated. In the present article for each possible for the system case, when a) a combination of expansions of right parts into irresolvable real multipliers is fixed, and b) a circular sequence of straight lines determined by these multipliers is fixed, topological types of all existing singular points of the system are described.

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