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A finiteness problem for one-dimensional maps


Author: W. de Melo
Journal: Proc. Amer. Math. Soc. 101 (1987), 721-727
MSC: Primary 58F12
DOI: https://doi.org/10.1090/S0002-9939-1987-0911040-1
MathSciNet review: 911040
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Abstract: We discuss the connection between the density of structurally stable maps in the space of unimodal maps of the interval, the finiteness of attractors and the nonexistence of wandering intervals. We show that in the space of unimodal maps having an eventually periodic flat critical point, there is a residual subset whose maps have infinitely many sinks. In this space there are also maps having a wandering interval.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0911040-1
Keywords: Unimodal maps, structural stability, wandering intervals, sinks, attractors, critical point
Article copyright: © Copyright 1987 American Mathematical Society

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