To fixpoint



Keywords: to fixpoint
Description: The fixed point of a function starting from an initial value can be computed in the Wolfram Language using FixedPoint [ f . x ]. Similarly, to get a list of the values obtained by iterating

The fixed point of a function starting from an initial value 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.

If a variable is slightly displaced from a fixed point, it may (1) move back to the fixed point ("asymptotically stable" or "superstable"), (2) move away ("unstable"), or (3) move in a neighborhood of the fixed point but not approach it ("stable" but not "asymptotically stable"). Fixed points are also called critical points or equilibrium points. If a variable starts at a point that is not a critical point. it cannot reach a critical point in a finite amount of time. Also, a trajectory passing through at least one point that is not a critical point cannot cross itself unless it is a closed curve. in which case it corresponds to a periodic solution.




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