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The topological complexity of Cantor attractors for unimodal interval maps


Authors: Simin Li and Weixiao Shen
Journal: Trans. Amer. Math. Soc. 368 (2016), 659-688
MSC (2010): Primary 37E05; Secondary 37C70, 37B40
DOI: https://doi.org/10.1090/S0002-9947-2015-06372-7
Published electronically: February 3, 2015
MathSciNet review: 3413879
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Abstract: For a non-flat $ C^3$ unimodal map with a Cantor attractor, we show that for any open cover $ \mathcal U$ of this attractor, the complexity function $ p(\mathcal U, n)$ is of order $ n\log n$. In the appendix, we construct a non-renormalizable map with a Cantor attractor for which $ p(\mathcal {U}, n)$ is bounded from above for any open cover $ \mathcal {U}$.


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Additional Information

Simin Li
Affiliation: Department of Mathematics, University of Science and Technology of China, and Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Hefei, 230026, People’s Republic of China
Email: lsm@ustc.edu.cn

Weixiao Shen
Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076
Email: matsw@nus.edu.sg

DOI: https://doi.org/10.1090/S0002-9947-2015-06372-7
Received by editor(s): December 16, 2012
Received by editor(s) in revised form: December 2, 2013
Published electronically: February 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society