Bizarre topology is natural in dynamical systems
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- by Judy A. Kennedy and James A. Yorke PDF
- Bull. Amer. Math. Soc. 32 (1995), 309-316 Request permission
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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 32 (1995), 309-316
- MSC: Primary 58F12; Secondary 54F15, 54F50, 54G15, 58F13
- DOI: https://doi.org/10.1090/S0273-0979-1995-00599-9
- MathSciNet review: 1307903