One-dimensional Dynamics for a Discontinuous Singular Map and the Routes to Chaos

We visit a previously proposed discontinuous, two-parameter generalization of thecontinuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points x 0 . 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 = ±8 as accumulation points, where every neighborhood contains infinitely many points generated by the map