Abstract
In this paper we study a stratum of integrable cubic vector fields with a saddle singularity having symmetry, i.e. symmetric with respect to two axes. Our perspective is from the point of view of invariant algebraic curves of the systems. We study the global geometry of such systems. We give the bifurcation diagram of the phase portraits of the vector fields. All bifurcations correspond to bifurcations of invariant algebraic curves. We next try to link this bifurcation diagram with the one given by Rousseau and Schlomiuk for integrable cubic vector fields with a centre singularity having symmetry.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
