  Chebyshev maps in the complex plane are typical chaotic maps. Veselov
generalized these map. We consider a class of those maps and view them as
holomorphic endomorphisms on the 3-dimensional complex projective space and
make use of the theory of complex dynamics in higher dimension. We determine
Julia sets and external rays of those maps, exactly. In the Julia sets, Moebius
strip and a special ruled surface appear. We also show some relation between
those maps and binary quartic forms.
