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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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Topological conditions for the existence of absorbing Cantor sets
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by Henk Bruin PDF
Trans. Amer. Math. Soc. 350 (1998), 2229-2263 Request permission

Abstract:

This paper deals with strange attractors of S-unimodal maps $f$. It generalizes earlier results in the sense that very general topological conditions are given that either

  1. [i)] guarantee the existence of an absorbing Cantor set provided the critical point of $f$ is sufficiently degenerate, or

  2. [ii)] prohibit the existence of an absorbing Cantor set altogether.

As a by-product we obtain very weak topological conditions that imply the existence of an absolutely continuous invariant probability measure for $f$.

References
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Additional Information
  • Henk Bruin
  • Affiliation: Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden
  • MR Author ID: 329851
  • Email: bruin@math.kth.se
  • Received by editor(s): June 1, 1995
  • Additional Notes: Supported by the Netherlands Organization for Scientific Research (NWO). The research for this paper was carried out during the author’s stay at the University of Erlangen-Nürnberg.
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2229-2263
  • MSC (1991): Primary 58F13, 58F11
  • DOI: https://doi.org/10.1090/S0002-9947-98-02109-6
  • MathSciNet review: 1458316