  We introduce Schottky maps-conformal maps between relative Schottky sets, and
study their local rigidity properties. This continues the investigations of
relative Schottky sets initiated in [S. Merenkov, "Planar relative Schottky
sets and quasisymmetric maps", Proc. London Math. Soc. (3) 104 (2012),
455-485]. Besides being of independent interest, the latter and current works
provide key ingredients in the forthcoming proof of quasisymmetric rigidity of
Sierpi\'nski carpet Julia sets of rational functions.
