Invariant circles and phase portraits of cubic vector fields on the sphere

Joji Benny, Supriyo Jana, Soumen Sarkar

In this paper, we characterize and study dynamical properties of cubic vector fields on the sphere ${\mathbb{S}}^2=\{(x,y,z)\in {\mathbb{R}}^3|x^2+y^2+z^2=1\}$. We start by…