TITLE: A numerical method for computing unstable quasi-periodic solutions for the 2--D Poiseuille flow AUTHORS: Pablo S. Casas^(1), Angel Jorba^(2) (1) Departament de Matem\`atica Aplicada I, Universitat Polit\`ecnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain). (2) Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona (Spain). E-mails: pablo@vilma.upc.es, angel@maia.ub.es ABSTRACT: We study the dynamics of two-dimensional Poiseuille flow. Firstly we obtain the family of periodic solutions which bifurcates from the laminar flow, together with its stability for several values of the wave number $\alpha$. The curve of periodic flows presents several Hopf bifurcations. For $\alpha=1.02056$ we follow the branches of quasi-periodic orbits that are born at one of the bifurcation points.