Topological arguments combined with the uniqueness theorem require orbits to be created in a particular order as a function of increasing control parameter for the logistic map. The topological arguments involve the existence of paired points in saddle-node pairs of orbits which become degenerate at the saddle-node bifurcation, and the presence of one set of paired points between another. The uniqueness theorem forbids a single point to be an initial condition for two inequivalent orbits. It is possible, but not practical, to build up the unique order in which orbits are created using these arguments. A simpler way is available.
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