Centers for trigonometric Abel equations
The paper is concerned with various notions of (isochronous) centers for planar systems of the form \[ \dot x = -y +P(x,y),\; \dot y = x + Q(x,y),\tag{1} \] the main focus is on the notion of strongly persistent center and on a condition on the vanishing of some generalized moments for the Abel equation \[ \frac{d r}{d\theta} = A(\theta)r^3+B(\theta)r^2 \] (which is related to (1) in polar coordinates). Particular emphasis is given to the case when \(A\) and \(B\) are trigonometric polynomials.
scientific article; zbMATH DE number 6134564