Cubic differential systems with invariant straight lines of total multiplicity seven and four real distinct infinite singularities

Date

2021-10-03

Authors

Bujac, Cristina
Schlomiuk, Dana
Vulpe, Nicolae

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Publisher

Texas State University, Department of Mathematics

Abstract

In this article we consider the class CSL74s∞ of non-degenerate real planar cubic vector fields possessing four distinct real infinite singularities and invariant straight lines, including the line at infinity of total multiplicity 7. We prove that there are exactly 93 distinct configurations of invariant straight lines for this class, and present corresponding examples for the realization of each one of the detected configurations.

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Keywords

Cubic vector field, Invariant straight line, Multiplicity of singularity, Infinite and finite singularities, Multiplicity of invariant lines, Configurations of invariant straight lines

Citation

Bujac, C., Schlomiuk, D., & Vulpe, N. (2021). Cubic differential systems with invariant straight lines of total multiplicity seven and four real distinct infinite singularities. <i>Electronic Journal of Differential Equations, 2021</i>(83), pp. 1-110.

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Attribution 4.0 International

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