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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Pseudocircles in dynamical systems


Authors: Judy A. Kennedy and James A. Yorke
Journal: Trans. Amer. Math. Soc. 343 (1994), 349-366
MSC: Primary 58F15; Secondary 54F15, 54F50, 54H20, 58F20
MathSciNet review: 1187029
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1187029-5
Keywords: Indecomposable invariant set, pseudocircle, $ {C^\infty }$ map, perturbable dynamical system
Article copyright: © Copyright 1994 American Mathematical Society