On Ishii's equation (Q2487998)

The authors deal with the following so-called Ishii equation \[ \dot x_1= x_2,\quad \dot x_2= x_3,\quad \dot x_3= x_1 x_2.\tag{1} \] They show that (1) has a Hamilton-Poisson realization with a Hamiltonian \(H(x_1,x_2,x_3)\). The authors prove that the system (1) can be explicitly integrated via a Weierstrass function and study its dynamical behaviour as well.