Global dynamics of the two-dimensional dynamical systems of special type

We study parametic class of two-dimensional discrete dynamical systems, which is a generalization of renormalization group mapping in the hierarchical fermionic model. To analyze global dynamics we develop methods of computer geometry. We reduce original dynamical system to the quadratic projective map and realize two-dimensional projective space as a disk. All fixed points and some invariant sets are described explicitly. With the using of this information we describe the global dynamics of the mapping for selected domains of the parameter space.