Bifurcation diagram of a map with multiple critical points

In this work a conjecture to draw the bifurcation diagram of a map with multiple critical points is enunciated. The conjecture is checked by using two quartic maps in order to verify that the bifurcation diagrams obtained according to the conjecture contain all the periodic orbits previously counted by Xie and Hao for maps with four laps.

We show that a map with split bifurcation contains more periodic orbits than those counted by these authors for a map with the same number of laps.