How to find differential equation systems with isochrone centers?

35 Views Asked by At

We define the system

$$\begin{cases}\dot{x}=P(x,y) \\\dot{y}=Q(x,y)\end{cases}$$

with $P(x,y)$, $Q(x,y)$ polinomyals with degree $\leq 3$.

How can we find the general form of the family of systems that have an isochrone center?

On my notes we barely defined them, and it's written that it's a little bit difficult to find this set of differential equations. Is there any way to give a general form of systems with an isochrone center?

Thanks.