Stereographically conjugate differential systems
V.N. Gorbuzov
TL;DR
This paper develops a topological framework for analyzing second-order autonomous differential systems on spheres, introducing stereographic conjugation and examining trajectory behavior near infinity.
Contribution
It constructs a stereographic atlas of trajectories and establishes differential connections between conjugate systems, advancing global qualitative analysis methods.
Findings
Established topological bases for trajectory behavior on spheres.
Constructed a stereographic atlas of trajectories.
Analyzed behavior near infinitely remote points.
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.
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Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry