Phase Flows of One Family of Cubic Systems in a Poincare Circle. I.
<![CDATA[On a real (x,y)-plane a normal system of ordinary differential equations is considered, being the right parts are respectively quadratic and cubic forms of x and y with arbitrary constant coefficients. The task is to investigate the behavior of its trajectories on an extended (x,y)- plane or, in equivalent terms, in a Poincare circle. In Part I of this investigation all possible for this system topological types of a singular point O(0,0) are revealed, and criteria of their realization are formulated. Topological types of the point O are given: <ul> <li> in terms of bundles of O-semiorbits of the system of N (node) and S (saddle) types, and</li> <li> in terms of O-sectors of Bendixon of E (elliptic), H (hyperbolic) and P (parabolic) types. </li> </ul>]]>