Dynamics
Two humps and one entropy
A map of an interval with one hump has its chaos measured by one number, the entropy, and that number never decreases as the hump rises. Give the map two turning points — a hump and a dip — and the parameter space becomes a plane. The entropy is no longer a function of one setting, and the question becomes whether the maps of a given entropy form one connected curve or several. John Milnor conjectured one. Counting the laps of every cubic's iterates exactly, over the whole plane of hump heights and dip depths, draws the curves — and each comes out whole.
