Limit sets

cluster point in a topological space

fractal set named after Gaston Maurice Julia

right|thumb|upright=1.5|Visual representation of a [[#Strange_attractor|strange attractor. Another visualization of the same 3D attractor is this video. Code capable of rendering this is available.]] In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.

part of mathematics

closed trajectory in a 2d phase space of a dynamical system such that that another trajectory spirals into it as time approaches ±∞

state a dynamical system reaches after an infinite amount of time has passed, by either going forward or backwards in time

point that returns to itself after function iteration

Fatou component

fixed point that does not have any center manifolds

fractal related to the mandelbrot set

portion of phase space of a dynamical system that exhibits stable motion