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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Critical points of one parameter families of maps of the interval


Author: Louis Block
Journal: Proc. Amer. Math. Soc. 88 (1983), 347-350
MSC: Primary 58F14; Secondary 58F20
MathSciNet review: 695273
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Abstract: It is shown that some of the periodic phenomena which is well known to occur for the critical point of the quadratic family $ {f_s}(x) = sx(1 - x)$ (and other $ {C^1}$ families with a single critical point) occurs for each critical point in $ {C^1}$ families with an arbitrary (possibly infinite) number of critical points. Also, some of the same behavior occurs in families of maps (which are not necessarily differentiable) where a critical point has derivative zero on either the left or the right side. A stronger condition is obtained when the derivative on the right is zero.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0695273-4
PII: S 0002-9939(1983)0695273-4
Article copyright: © Copyright 1983 American Mathematical Society