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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Smooth dynamics on Weierstrass nowhere differentiable curves


Authors: Brian R. Hunt and James A. Yorke
Journal: Trans. Amer. Math. Soc. 325 (1991), 141-154
MSC: Primary 58F13; Secondary 54H20
MathSciNet review: 1040043
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Abstract: We consider a family of smooth maps on an infinite cylinder which have invariant curves that are nowhere smooth. Most points on such a curve are buried deep within its spiked structure, and the outermost exposed points of the curve constitute an invariant subset which we call the "facade" of the curve. We find that for surprisingly many of the maps in the family, all points in the facades of their invariant curves are eventually periodic.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1040043-X
PII: S 0002-9947(1991)1040043-X
Article copyright: © Copyright 1991 American Mathematical Society