What is generic?
(Thanks to Hawley Rising for contributing to this answer) Generic in dynamical systems is intended to convey “usual” or, more properly, “observable”. Roughly speaking, a property is generic over a class if any system in the class can be modified ever so slightly (perturbed), into one with that property. The formal definition is done in the language of topology: Consider the class to be a space of systems, and suppose it has a topology (some notion of a neighborhood, or an open set). A subset of this space is dense if its closure (the subset plus the limits of all sequences in the subset) is the whole space. It is open and dense if it is also an open set (union of neighborhoods). A set is countable if it can be put into 1-1 correspondence with the counting numbers. A countable intersection of open dense sets is the intersection of a countable number of open dense sets. If all such intersections in a space are also dense, then the space is called a Baire space, which basically means it i
