English Dictionary

accumulation point

noun

(topology, "of" a subset of a topological space) Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S.

An accumulation point is a point in a topological space where every neighborhood of the point contains infinitely many points of the space.

意味（1）

(topology, "of" a subset of a topological space) Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S.

LEMMA 5.2 Let X be a Hausdorff space and A a subset of X. A point a∈X is an accumulation point of A if and only if a is a limit point of A.

意味（2）

(mathematical analysis, "of" a sequence) Given a sequence sᵢ, a point x whose every neighborhood contains at least one element of the sequence distinct from x.

意味（3）

(systems theory, dynamical systems, chaos theory) For certain maps, a point beyond which periodic orbits give way to chaotic ones.

The chaotic set (not necessarily attracting) is formed after the first accumulation point (a_∞≈3.570 for the logistic mapping) is reached. In the chaotic region of the logistic map the periodicity re-emerges in periodic windows which are bounded by the accumulation point from the right and by the saddle-node bifurcation from the left. A reverse bifurcation sequence occurs above the accumulation point.