First integrals and phase portraits of planar polynomial differential cubic systems with invariant straight lines of total multiplicity eight

Cristina Bujac,Nicolae Vulpe

doi:10.14232/ejqtde.2017.1.85

Abstract

First integrals and phase portraits of planar polynomial differential cubic systems with invariant straight lines of total multiplicity eight

Highlights

15(2016), 327–348] all first integrals and phase portraits were constructed for the family of cubic differential systems with the maximum number of invariant straight lines, i.e. 9 (considered with their multiplicities)
Polynomial differential systems on the plane are systems of the form x = P(x, y), y = Q(x, y), (1.1)where P, Q ∈ R[x, y], i.e. P and Q are the polynomials over R
Syst. 15(2016), 327–348] all first integrals and phase portraits were constructed for the family of cubic differential systems with the maximum number of invariant straight lines, i.e. 9

Summary

Introduction

15(2016), 327–348] all first integrals and phase portraits were constructed for the family of cubic differential systems with the maximum number of invariant straight lines, i.e. 9 (considered with their multiplicities). In Theorem 3.1 we describe all the 51 possible configurations of invariant lines which could possess the cubic systems in the class CSL8.

Objectives

Results

Conclusion