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Topological and metrical conditions for Collet-Eckmann unimodal maps

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Abstract

In this paper we prove that Sands' topological condition for Collet-Eckmann maps implies Tsujii's metrical condition; on the other hand, if a Collet-Eckmann map satisfies Tsujii's metrical condition, then it satisfies Sands' topological condition. Thus we obtain three different versions of Benedicks-Carleson Theorem by using topological conditions.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, 100080, Beijing, China

    Wang Lanyu

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  1. Wang Lanyu
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Additional information

This research is supported by the National Natural Science Foundation of China (No. 19901035) and TWAS/CNPq associate fellowship.

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Lanyu, W. Topological and metrical conditions for Collet-Eckmann unimodal maps. Acta Mathematicae Applicatae Sinica 17, 350–360 (2001). https://doi.org/10.1007/BF02677379

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  • DOI: https://doi.org/10.1007/BF02677379

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