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<p>We study the farthest point mapping on the boundary of the 4-cube with respect to the intrinsic metric, and its dynamics as a piecewise rational map. It is shown that its limit set is the union of the main diagonals of eight facets. If the source point is in the interior of a facet, its limit set is also in the interior of a facet.</p>

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The farthest point map on the 4-cube

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Yoshikazu Yamagishi

摘要

We study the farthest point mapping on the boundary of the 4-cube with respect to the intrinsic metric, and its dynamics as a piecewise rational map. It is shown that its limit set is the union of the main diagonals of eight facets. If the source point is in the interior of a facet, its limit set is also in the interior of a facet.