Structurally stable

Roughly speaking, an appropriate topology is placed on the space of all systems under consideration. A given system is called structurally stable if it has a neighborhood in the space such that every system within that neighborhood is topologically conjugate

to the given system.

Besides being an elegant and interesting way to view dynamical systems, this concept can be justified as important outside of mathematics for the following reason. Since it is impossible to know a system exactly, it is imprudent to concentrate on those properties of a system which are not shared by nearby systems. Since all of the topological properties of a structurally stable system are shared by its neighbors, such systems are important to study.