Infinitely Remote Singularities of Special Differential Dynamic Systems

Abstract

The work is devoted to the results of a fundamental study on the arithmetical plane of a broad special family of differential dynamic systems having polynomial right parts. Let those polynomials be a cubic and a square reciprocal forms. A task of a whole investigation was to find out all topologically different phase portraits in a Poincare circle and indicate close to coefficient criteria of them. To achieve this goal a Poincare method of the central and the orthogonal consecutive displays (or mappings) has been used. As a rezult more than 250 topologically different phase portraits in a total have been constructed. Every portrait we depict with a special table called a descriptive phase portrait. Each line of such a special table corresponds to one invariant cell of the phase portrait and describes its boundary, a source of its phase flow and a sink of it. All finite and infinitely remote singularities of dynamic systems under consideration were fully investigated. Namely infinitely remote singularities are discussed in the present article.

Keywords

• Dynamic systems,Phase portraits,Phase flows,Poincare sphere,Poincare circle,Singular points,Separatrices,Trajectories

References

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