  Topological bases of behaviour of trajectories for autonomous differential
systems of the second order on the projective phase plane are stated. By means
of Poincare's circles the projective atlas of trajectories is constructed.
Differential connections between trajectories of projectively conjugated
differential systems are established. The behaviour of trajectories in an
neighbourhood of infinitely remote straight line of the projective phase plane
and property of closed trajectories on the projective phase plane is
investigated. Examples of full qualitative research of trajectories of
differential systems on the projective phase plane are given.
