Formalization of the idea of an attractor or repellor in dynamical systems
In mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor. In the case of hyperbolic dynamics, the corresponding notion is that of the hyperbolic set.
Example hyperbolic flow, illustrating stable and unstable manifolds. The vector field equation is . The stable manifold is the x-axis, and the unstable manifold is the other asymptotic curve crossing the x-axis.
