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The Devil’s Staircase Dimensions and Measure-Theoretical Entropy of Maps with Horizontal Gap

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abstract

This work elucidates the measure-theoretical entropy and dimensions of a unimodal map with a horizontal gap. The measure-theoretical entropy and dimensions of the F t (which is defined later) are shown to form a devil’s staircase structure with respect to the gap size t. Pesin’s formula for gap maps is also considered.

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Authors and Affiliations

  1. National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu, Taiwan, 30043

    Jung-Chao Ban

  2. Department of Applied Mathematics, National Chiao-Tung University, Hsinchu, Taiwan

    Song-Sun Lin

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  1. Jung-Chao Ban
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  2. Song-Sun Lin
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Correspondence to Jung-Chao Ban or Song-Sun Lin.

Additional information

Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.

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Ban, JC., Lin, SS. The Devil’s Staircase Dimensions and Measure-Theoretical Entropy of Maps with Horizontal Gap. J Dyn Diff Equat 16, 833–846 (2004). https://doi.org/10.1007/s10884-004-6697-3

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  • DOI: https://doi.org/10.1007/s10884-004-6697-3

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