Critical curves and 2D coupled maps

The theory of critical curves for maps of the plane provides p owerful tools for locating the chief characteristic features of a discret e dynamical system in two dimensions: the location of its chaotic attractors, its bas in boundaries, and the mecha- nisms of its bifurcations. Nowadays one begins to recognize the role played by critical curves of maps in the analysis, in the understanding and description of the bifurca- tions, and transition to chaotic behavior in coupled maps. I n this paper we consider some properties of such maps, which possess a chaotic attractor. Some examples are considered in this paper in which we can see the effective rol e played by such curves in bifurcation theory.