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Geometric properties of images of cartesian products of regular Cantor sets by differentiable real maps

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Abstract

We prove dimension formulas for arithmetic sums of regular Cantor sets, and, more generally, for images of cartesian products of regular Cantor sets by differentiable real maps.

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Authors and Affiliations

  1. SUSTech International Center for Mathematics, Shenzhen, Guangdong, People’s Republic of China

    Carlos Gustavo Moreira

  2. Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil

    Carlos Gustavo Moreira

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  1. Carlos Gustavo Moreira
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Correspondence to Carlos Gustavo Moreira.

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Dedicated to Jean-Christophe Yoccoz and Welington de Melo.

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Moreira, C.G. Geometric properties of images of cartesian products of regular Cantor sets by differentiable real maps. Math. Z. 303, 3 (2023). https://doi.org/10.1007/s00209-022-03151-z

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  • DOI: https://doi.org/10.1007/s00209-022-03151-z

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