How are the rotation numbers associated to the primary bulbs arranged around the boundary of the main cardioid?
Amazingly, the order of the rotation numbers around the boundary of the main cardioid is exactly the same as the rational numbers. That is, if you call the “cusp” of the cardioid 0, and then proceed in the counterclockwise direction, you visit each bulb corresponding to rotation number p/q in exact order, ending at 1 when you arrive back at the cusp. Equally amazingly, all you need to prove this is a little (complex) calculus!
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