TITLE: Numerical study of bifurcations for the 2--D Poiseuille problem 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 check our calculations with previous results concerning the laminar solution and the minimum Reynolds number such that it becomes unstable. Next we studied time periodic solutions which, because of the imposed periodicity in the stream-wise direction, are rotating waves, what allow us to treat them as stationary flows in a moving system of reference. We use this fact to obtain also unstable time periodic flows and bifurcation branches from the laminar solution for different values of the wave number. Finally we introduce the case of bifurcation to quasi-periodic solutions.