Smooth Dynamics on Weierstrass Nowhere Differentiable Curves

Brian R. Hunt and James A. Yorke

Trans. Amer. Math. Soc. 325 (1991), 141-154.

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.

Click here for an online copy of this paper from JSTOR.

Back to my list of recent papers.

Back to my home page.

Last updated: June 23, 1998