The Hausdorff dimension of chaotic sets for interval self-maps |
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| Authors: | Huoyun Wang Jincheng Xiong |
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| Affiliation: | a Department of Mathematics of Guangzhou University, Guangzhou 510405, People's Republic of China
b Department of Mathematics, South China Normal University, Guangzhou 510631, People's Republic of China |
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| Abstract: | We obtain two sufficient conditions for an interval self-map to have a chaotic set with positive Hausdorff dimension. Furthermore, we point out that for any interval Lipschitz maps with positive topological entropy there is a chaotic set with positive Hausdorff dimension. |
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| Keywords: | primary, 37E10 secondary, 54H20 |
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