TY  - JOUR
T1  - Infinitely Remote Singularities of Special Differential Dynamic Systems
AU  - Andreeva, İrina
PY  - 2018
DA  - December
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 1
EP  - 7
IS  - 4
LA  - en
AB  - The work is devoted to the results of a fundamental study on thearithmetical plane of a broad special family of differential dynamic systemshaving polynomial right parts. Let those polynomials be a cubic and a squarereciprocal forms. A task of a whole investigation was to find out alltopologically different phase portraits in a Poincare circle and indicate closeto coefficient criteria of them. To achieve this goal a Poincare method of thecentral and the orthogonal consecutive displays (or mappings) has been used. Asa rezult more than 250 topologically different phase portraitsin a total have been constructed. Every portrait we depict with a special tablecalled a descriptive phase portrait. Each line of such a special tablecorresponds to one invariant cell of the phase portrait and describes itsboundary, a source of its phase flow and a sink of it. All finite andinfinitely remote singularities of dynamic systems under consideration werefully investigated. Namely infinitely remote singularities are discussed in thepresent article.
KW  - Dynamic systems
KW  - Phase portraits
KW  - Phase flows
KW  - Poincare sphere
KW  - Poincare circle
KW  - Singular points
KW  - Separatrices
KW  - Trajectories
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UR  - https://dergipark.org.tr/en/pub/epstem/issue//492290
L1  - https://dergipark.org.tr/en/download/article-file/588635
ER  -