A genealogy for finite kneading sequences of bimodal maps on the interval

Ringland, John; Tresser, Charles

doi:10.1090/S0002-9947-1995-1311914-5

A genealogy for finite kneading sequences of bimodal maps on the interval
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Trans. Amer. Math. Soc. 347 (1995), 4599-4624 Request permission

Abstract:

We generate all the finite kneading sequences of one of the two kinds of bimodal map on the interval, building each sequence uniquely from a pair of shorter ones. There is a single pair at generation $0$, with members of length $1$. Concomitant with this genealogy of kneading sequences is a unified genealogy of all the periodic orbits. (See Figure 0.) Figure 0. Loci of some finite kneading sequences for a two-parameter cubic family

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