Pseudocircles in dynamical systems

Kennedy, Judy A.; Yorke, James A.

doi:10.1090/S0002-9947-1994-1187029-5

Pseudocircles in dynamical systems
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by Judy A. Kennedy and James A. Yorke PDF

Trans. Amer. Math. Soc. 343 (1994), 349-366 Request permission

Abstract:

We construct an example of a ${C^\infty }$ map on a 3-manifold which has an invariant set with an uncountable number of components, each of which is a pseudocircle. Furthermore, any map which is sufficiently close (in the ${C^1}$-metric) to the constructed map has a similar set.

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