The phase portrait of the Hamiltonian system associated to a Pinchuk map

<div><p>Abstract In this paper we describe the global phase portrait of the Hamiltonian system associated to a Pinchuk map in the Poincaré disc. In particular, we prove that this phase portrait has 15 separatrices, five of them singular points, and 7 canonical regions, six of them of type strip and one annular.</p></div>