Published August 31, 2013
| Version v1
Journal article
On the structure of self-affine convex bodies
Creators
- 1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Description
We study the structure of convex bodies in Rd 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≥3 and derive a detailed description of self-affine bodies in R3. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument. Bibliography: 10 titles
Availability note (English)
Available from http://dx.doi.org/10.1070/SM2013v204n08ABEH004332Additional details
Identifiers
Publishing Information
- Journal Title
- Sbornik. Mathematics
- Journal Volume
- 204
- Journal Issue
- 8
- Journal Page Range
- p. 1122-1130
- ISSN
- 1064-5616
INIS
- Country of Publication
- United States
- Country of Input or Organization
- International Atomic Energy Agency (IAEA)
- INIS RN
- 46024112
- Subject category
- S97: MATHEMATICAL METHODS AND COMPUTING;
- Resource subtype / Literary indicator
- Bibliography
- Descriptors DEI
- BIBLIOGRAPHIES; EQUATIONS; MATHEMATICAL OPERATORS
- Descriptors DEC
- DOCUMENT TYPES