J. Sanchez a,*, M. Net a, B. Garcıa-Archilla b, C. Simo c

methods. A thermal convection fluid dynamics problem, which has a rich bifurcation diagram due to symmetries, has 4 changes of stability when the parameters on which the problem depends are varied. Unstable manifolds must also be calculated because they may drive the dynamics of the system or give rise to stable solutions as will be seen in the examples shown here. Some of these tasks are now almost routinely performed for low-dimensional problems. Many researchers in dynamical systems have benefited from the availability of*been used as test. After a pseudo-spectral discretization of the equations a system of dimension O(10) has been ob-tained. The efficiency of the algorithms, which allows the unfolding of a complex diagram of periodic orbits, makes the methods suitable for the study of large nonlinear dissipative partial differential equations