Planar nonautonomous polynomial equations. III: Zeros of the vector field (Q1947831)

Theorems on existence and multiplicity of \(T\)-periodic solutions and their heteroclinic conections of planar equations of the form \[ \dot z=\sum_{j=0}^n a_j(t)z^j \] are given. It is assumed \(a_j: \mathbb R\to \mathbb C\) are \(T\)-periodic and continuous. Proofs are based on the Denjoy-Wolff fixed point theorem and geometric arguments.