ABSTRACT
The existence of chaotic attracting sets has had an important impact in the natural sciences. For a discipline that has built its cultural power through history on reproducibility, this is quite a revolution. The flow of the laser model can be explained in terms of a two-dimensional (2-d) Poincaré map, while kneading theory was conceived for one-dimensional (1-d) maps. Certainly, the search for an order organization in 2-d maps similar to the kneading theory in 1-d maps requires new tools. In general, three-dimensional dynamical systems will have many coexisting periodic solutions. If a system has a strange attractor as a solution, there will be infinitely many coexisting periodic solutions. The horseshoe map is a key element to understand in dynamics as the complexity it displays can be observed in any map with transverse homoclinic points. The simple observation allows us to compute algorithmically the linking and knot properties of the periodic solutions of the 2-d map.
