Stereographically conjugate differential systems

Abstract

Topological bases of behaviour of trajectories for autonomous differential systems of the second order on sphere are stated. Stereographic atlas of trajectories is constructed. Differential connections between trajectories of stereographically conjugate differential systems are established. The behaviour of trajectories in an neighbourhood of infinitely remote point of the phase plane is investigated. Examples of global qualitative research of trajectories of stereographically conjugate differential systems are given.