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."

Return to dynamics and number theory.