  Propagation of waves through Cantor-set media is investigated by
renormalization-group analysis. For specific values of wave numbers,
transmission coefficients are shown to be governed by the logistic map, and in
the chaotic region, they show sensitive dependence on small changes of
parameters of the system such as the index of refraction. For other values of
wave numbers, our numerical results suggest that light transmits completely or
reflects completely by the Cantor-set media ${\rm C}_{\infty}$. It is also
shown that transmission coefficients exhibit a local scaling behavior near
complete transmission if the complete transmission is achieved at a wave number
$\kappa=\kappa^*$ with a rational $\kappa^*/\pi$. The scaling function is
obtained analytically by using the Euler's totient function, and the local
scaling behavior is confirmed numerically.
