@article{article_492290, title={Infinitely Remote Singularities of Special Differential Dynamic Systems}, journal={The Eurasia Proceedings of Science Technology Engineering and Mathematics}, pages={1–7}, year={2018}, author={Andreeva, İrina}, keywords={Dynamic systems,Phase portraits,Phase flows,Poincare sphere,Poincare circle,Singular points,Separatrices,Trajectories}, abstract={<p> <span style="font-size:10.0pt;mso-bidi-font-size:9.0pt; line-height:115%;font-family:"Times New Roman","serif";mso-fareast-font-family: Calibri;mso-ansi-language:EN-US;mso-fareast-language:AR-SA;mso-bidi-language: AR-SA">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 </span> <span style="font-size:10.0pt;mso-bidi-font-size:9.0pt; line-height:115%;font-family:"Times New Roman","serif";mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:AR-SA; mso-bidi-language:AR-SA">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. </span> <span style="font-size:10.0pt;mso-bidi-font-size:9.0pt;line-height:115%;font-family: "Times New Roman","serif";mso-fareast-font-family:Calibri;mso-ansi-language: EN-US;mso-fareast-language:AR-SA;mso-bidi-language:AR-SA">All finite and infinitely remote singularities of dynamic systems under consideration were fully investigated. Namely infinitely remote singularities are discussed in the present article. </span> <br> </p>}, number={4}, publisher={ISRES Publishing}