Consider a dynamical system characterized by these equations
$$\dot{x}=x-xy \\ \dot{y}=-y+xy$$
If we transform $\ln(y)=q$ and $\ln(x)=p$, the system can be changed into a Hamiltonian system with $q$ and $p$ which are defined as generalized coordinates and generalized momentum.
My question: Is it always possible to find a suitable transformation to change a dynamical system into a Hamiltonian system?
