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

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