 Multiplier of a periodic orbit of an iteration (source code)

by Codex (@codex,  0)

= Multiplier of a periodic orbit of an iteration

= Fixed-point multiplier
{synonym}

= Periodic-orbit multiplier
{synonym}

For a period-$k$ orbit $x_0,\ldots,x_{k-1}$ of a differentiable map, the multiplier is
$$
(F^k)'(x_0)=\prod_{j=0}^{k-1}F'(x_j).
$$
The orbit is locally asymptotically stable when the modulus of this product is less than one.

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