Topological and metrical conditions for Collet-Eckmann unimodal maps |
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| Authors: | Wang Lanyu |
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| Institution: | (1) Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, 100080 Beijing, China |
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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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| Keywords: | Unimodal map Collet-Eckmann map Schwarzian derivative Kneading invariant |
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