Bizarre topology is natural in dynamical systems
Abstract
We describe an example of a C∞ 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 C1 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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