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Bizarre topology is natural in dynamical systems

Judy A. Kennedy·James A. Yorke
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Abstract

We describe an example of a $C^\infty$ diffeomorphism on a 7--manifold which has a compact invariant set such that uncountably many of its connected components are pseudocircles. (Any 7--manifold will suffice.) Furthermore, any diffeomorphism which is sufficiently close (in the $C^1$ metric) to the constructed map has a similar invariant set, and the dynamics of the map on the invariant set are chaotic.

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Judy A. Kennedy, James A. Yorke. 1995-07-01. Bizarre topology is natural in dynamical systems. https://arxiv.org/abs/math/9507223

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