TITLE: Unstable manifolds computation for the two-dimensional plane Poiseuille flow AUTHORS: Pablo S. Casas^(1), Angel Jorba^(2) (1) pablo@casas.upc.es Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain). (2) angel@maia.ub.es Departament de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona (Spain). ABSTRACT: We follow the unstable manifold of periodic and quasi-periodic solutions in time for the Poiseuille problem, using two formulations: holding constant flux or mean pressure gradient. By means of a numerical integrator of the Navier-Stokes equations, we let the fluid evolve from an initially perturbed unstable solution until the fluid reaches an attracting state. Thus, we detect several connections among different configurations of the flow such as laminar, periodic, quasi-periodic with 2 or 3 basic frequencies, and more complex sets that we have not been able to classify. Those connections make possible the location of new families of solutions, hard to find by means of numerical continuation of curves, and shows the richness of the dynamics of the Poiseuille flow.