  We visit a previously proposed discontinuous, two-parameter generalization of
the continuous, one-parameter logistic map and present exhaustive numerical
studies of the behavior for different values of the two parameters and initial
points. In particular, routes to chaos exist that do not exhibit
period-doubling whereas period-doubling is the sole route to chaos in the
logistic map. Aperiodic maps are found that lead to cobwebs with x = infinity
as accumulation points, where every neighborhood contains infinitely many
points generated by the map.
