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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Authors: John Ringland and Charles Tresser
Journal: Trans. Amer. Math. Soc. 347 (1995), 4599-4624
MSC: Primary 58F03; Secondary 58F14
MathSciNet review: 1311914
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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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Article copyright: © Copyright 1995 American Mathematical Society