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This article is cited in 3 scientific papers (total in 3 papers)
On the structure of self-affine convex bodies
A. S. Voynov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
We study the structure of convex bodies in $\mathbb R^d$ that can be represented as a union of their affine images with no common interior points. Such bodies are called self-affine. Vallet's conjecture on the structure of self-affine bodies was proved for $d = 2$ by Richter in 2011. In the present paper we disprove the conjecture for all $d \geqslant 3$ and derive a detailed description of self-affine bodies in $\mathbb R^3$. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument.
Bibliography: 10 titles.
Keywords:
partition, self-affine set, convex polyhedron.
Received: 30.08.2012
Citation:
A. S. Voynov, “On the structure of self-affine convex bodies”, Mat. Sb., 204:8 (2013), 41–50; Sb. Math., 204:8 (2013), 1122–1130
Linking options:
https://www.mathnet.ru/eng/sm8169https://doi.org/10.1070/SM2013v204n08ABEH004332 https://www.mathnet.ru/eng/sm/v204/i8/p41
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Abstract page: | 400 | Russian version PDF: | 182 | English version PDF: | 7 | References: | 48 | First page: | 24 |
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