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iterated_function [2013/09/09 15:52] nikolaj |
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| - | ===== Iterated function ===== | ||
| - | ==== Definition ==== | ||
| - | | $ f:X\to X $ | | ||
| - | | $ n\in \mathbb N, n\neq 0 $ | | ||
| - | ^ $ f^n $ ^ | ||
| - | |||
| - | ^ $ f^1=f $ ^ | ||
| - | ^ $ f^{n}=f\circ f^{n-1} $ ^ | ||
| - | |||
| - | ==== Ramifications ==== | ||
| - | === Predicates === | ||
| - | We call a function //idempotent// if $f^2=f$. We say it's an //involution// if $f^2=\text{id}$. | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Unary operation]] | ||
| - | === Requirements === | ||
| - | [[Relation concatenation]], | ||
| - | [[Natural number]] | ||
