  We study a possible superconductivity in quasiperiodic systems, by portraying
the issue within the attractive Hubbard model on a Penrose lattice. Applying a
real-space dynamical mean-field theory to the model consisting of 4181 sites,
we find a superconducting phase at low temperatures. Reflecting the
nonperiodicity of the Penrose lattice, the superconducting state exhibits an
inhomogeneity. According to the type of the inhomogeneity, the superconducting
phase is categorized into three different regions which cross over each other.
Among them, the weak-coupling region exhibits spatially extended Cooper pairs,
which are nevertheless distinct from the conventional pairing of two electrons
with opposite momenta.
