Stereographically conjugate differential systems
Dynamical Systems
2015-03-05 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.1503.01426,
title = {Stereographically conjugate differential systems},
author = {V. N. Gorbuzov},
journal= {arXiv preprint arXiv:1503.01426},
year = {2015}
}
Comments
31 pages, 59 figures. English and Russian versions