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
Abstract: It is shown that some of the periodic phenomena which is well known to occur for the critical point of the quadratic family (and other families with a single critical point) occurs for each critical point in 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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