Something dynamics can tell us about number theory

Review of fixed points

A fixed point of f is a point x* left unchanged by f: f(x*) = x*.

Graphical iteration reveals a geometric characterization of fixed points. The fixed points of f are exactly the points where the graph of f intersects the diagonal line.

Any interesction point of the graph and the diagonal does not move under "vertically to the graph, horizontally to the diagonal."

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