Projective atlas of trajectories of differential systems
Dynamical Systems
2014-01-07 v1 Classical Analysis and ODEs
Abstract
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.
Keywords
Cite
@article{arxiv.1401.1000,
title = {Projective atlas of trajectories of differential systems},
author = {V. N. Gorbuzov},
journal= {arXiv preprint arXiv:1401.1000},
year = {2014}
}
Comments
61 pages, 70 figures