The goal of this paper is to construct explicitly the global attractors of quasilinear parabolic equations, as it was done for the semilinear case by Brunovský and Fiedler (1986), and generalized by Fiedler and Rocha (1996). In particular, we construct heteroclinic connections between hyperbolic equilibria, stating necessary and sufficient conditions for heteroclinics to occur. Such conditions can be computed through a permutation of the equilibria. Lastly, an example is computed yielding the well known Chafee-Infante attractor.

21 pages, 1 figure