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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Bizarre topology is natural in dynamical systems


Authors: Judy A. Kennedy and James A. Yorke
Journal: Bull. Amer. Math. Soc. 32 (1995), 309-316
MSC: Primary 58F12; Secondary 54F15, 54F50, 54G15, 58F13
MathSciNet review: 1307903
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1995-00599-9
PII: S 0273-0979(1995)00599-9
Keywords: Indecomposable continuum, hereditarily indecomposable continuum, dynamical system, complicated invariant set, $ {C^{\infty}}$
Article copyright: © Copyright 1995 American Mathematical Society