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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Pseudocircles in dynamical systems
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by Judy A. Kennedy and James A. Yorke PDF
Trans. Amer. Math. Soc. 343 (1994), 349-366 Request permission

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
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 349-366
  • MSC: Primary 58F15; Secondary 54F15, 54F50, 54H20, 58F20
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1187029-5
  • MathSciNet review: 1187029