Jacobian pairs and Hamiltonian flows (Q674477)

Let \((f,g):\mathbb{C}^2\to\mathbb{C}^2\) be a polynomial mapping with a non-zero constant jacobian. The jacobian conjecture asserts that then \((f,g)\) has a polynomial inverse. The author gives several conditions for the invertibility of \((f,g)\) in terms of flows of the vector field \((-f_y,f_x)\).