Why is it sufficient to check at one point on the orbit to determine the hyperbolicity?

Question

In this Wikipedia entry on hyperbolic sets of dynamical systems, on the examples section, it was asserted that "more generally, a periodic orbit of $f$ with period $n$ is hyperbolic if and only if $Df^n$ at any point of the orbit has no eigenvalue with absolute value 1, and it is enough to check this condition at a single point of the orbit." I am confused of why it is sufficient to only check at one point.