[2.14] 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 w ith that property. The formal definition is done in the language of topology: Consider the clas s 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 closur e (the subset plus the limits of all sequences in the subset) is the whole s pace. 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 coun ting numbers. A countable intersection of open dense sets is the intersectio n of a countable number of open dense sets. If all such intersections in a s pace are also dense, then the space is called a Baire space, which basically means it is big enough. If we have such a Baire space of dynamical systems, and there is a property which is true on a countable intersection of open d ense sets, then that property is generic. If all this sounds too complicated, think of it as a precise way of defining a set which is near every system in the collection (dense), which isn't too big (need not have any "regions" where the property is true for every syste m). Generic is much weaker than "almost everywhere" (occurs with probability 1), in fact, it is possible to have generic properties which occur with pro bability zero. But it is as strong a property as one can define topologicall y, without having to have a property hold true in a region, or talking about measure (probability), which isn't a topological property (a property prese rved by a continuous function). -- 在细雨的午後 书页里悉哩哩地传来 " 周期3 = ? " 然而我知道 当我正在日耳曼深处的黑森林 继续发掘海森堡未曾做过的梦时 康德的诺言早已远离......... 远来的传教士静静地看着山涧不断反覆叠代自己的 过去 现在 和 未来 於是仅以 一颗量子浑沌 一本符号动力学 祝那发生在周一下午的新生 --

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