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Transactions of the American Mathematical Society

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



A complete classification of the piecewise monotone functions on the interval

Author: Stewart Baldwin
Journal: Trans. Amer. Math. Soc. 319 (1990), 155-178
MSC: Primary 58F08; Secondary 54H20, 58F13
MathSciNet review: 961618
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Abstract: We define two functions $ f$ and $ g$ on the unit interval $ [0,1]$ to be strongly conjugate iff there is an order-preserving homeomorphism $ h$ of $ [0,1]$ such that $ g = {h^{ - 1}}fh$ (a minor variation of the more common term "conjugate", in which $ h$ need not be order-preserving). We provide a complete set of invariants for each continuous (strictly) piecewise monotone function such that two such functions have the same invariants if and only if they are strongly conjugate, thus providing a complete classification of all such strong conjugacy classes. In addition, we provide a criterion which decides whether or not a potential invariant is actually realized by some piecewise monotone continuous function.

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Keywords: Topologically conjugate, kneading sequence
Article copyright: © Copyright 1990 American Mathematical Society

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