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Hausdorff dimension of Cantor intersections for coupled horseshoe maps

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 نشر من قبل Yoshitaka Saiki
 تاريخ النشر 2020
  مجال البحث فيزياء
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As a model to provide a hands-on, elementary understanding of chaotic dynamics in dimension 3, we introduce a $C^2$-open set of diffeomorphisms of whose cross sections are Cantor sets; the intersection of the unstable and stable sets contains a fractal set of Hausdorff dimension nearly $1$. Our proof employs the thicknesses of Cantor sets.



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