In the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds gives a formal mathematical definition to the general notions embodied in the idea of an attractor. In this work, we determine the stable and unstable manifolds of the normal form of the two-dimensional piecewise-linear maps in the neighborhood of a fixed point at the border using the stable manifold theorem. This is an important result about the structure of the set of orbits approaching to a hyperbolic fixed point.

stable and unstable manifolds, two-dimensional piecewise-linear, normal form maps.