Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] P. Collet and J.-P. Eckmann, Iterated maps on the interval as dynamical systems, Progress in Phys., vol. 1, Birkhauser, Basel, 1980. MR 613981 (82j:58078)
  • [2] R. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976), 459-467.
  • [3] J. Milnor and W. Thurston, On iterated maps of the interval. I: The kneading matrix; II: Periodic points, Preprint, Princeton, 1977. MR 970571 (90a:58083)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F14, 58F20

Retrieve articles in all journals with MSC: 58F14, 58F20

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society