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Transactions of the American Mathematical Society

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Genealogy of periodic points of maps of the interval

Author: Robert L. Devaney
Journal: Trans. Amer. Math. Soc. 265 (1981), 137-146
MSC: Primary 58F20; Secondary 28D99, 58F14
MathSciNet review: 607112
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Abstract: We describe the behavior of families of periodic points in one parameter families of maps of the interval which feature a transition from simple dynamics with finitely many periodic points to chaotic mappings. In particular, we give topological criteria for the appearance and disappearance of these families. Our results apply specifically to quadratic maps of the form $ {F_\mu }(x) = \mu x(1 - x)$.

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Article copyright: © Copyright 1981 American Mathematical Society

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