The fixed points of f can be found by a simple geometric property: they are the intersections of the graph of f and the diagonal. 
Cycles of f can be detected geometrically, by observing that points of an

For example, suppose 
f^{2}(x_{1}) = f(f(x_{1})) = f(x_{2}) = x_{1} 
Suppose x* is a fixed point of f^{2}. Then x* might 
belong to a 2cycle of f, or 
be a fixed point of f: if 
Suppose x* is a fixed point of f^{3}. Then x* might 
belong to a 3cycle of f, or 
be a fixed point of f 
Suppose x* is a fixed point of f^{4}. Then x* might 
belong to a 4cycle of f, or 
belong to a 2cycle of f: if 
be a fixed point of f 
In general, if x* is a fixed point of f^{n}, then x* belongs to an

As a consequence, if x* is a fixed point of f^{p} and p is prime,
then x* belongs to a 
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