invariant point

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 such that f(x_0) = x_0. The fixed point of a function f starting from an initial value x can be computed in the Wolfram Language using FixedPoint[f, x]. Similarly, to get a list of the values obtained by iterating the function until a fixed point is reached, the command FixedPointList[f, x] can be used. The following table lists the smallest positive fixed points for several simple functions.

Dottie number | elliptic fixed point | fixed point node | fixed point theorem | group fixed point | hyperbolic fixed point | Mann iteration | map fixed point | Newton's method | stable improper node | stable node | stable spiral point | stable star | unstable improper node | unstable node | unstable spiral point | unstable star