Fractal bodies invisible in 2 and 3 directions
Abstract
We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [A. Aleksenko and A. Plakhov. Bodies of zero resistance and bodies invisible in one direction. Nonlinearity 22, 1247-1258 (2009)], [A Plakhov and V Roshchina. Invisibility in billiards. Nonlinearity 24, 847-854 (2011)], where two-dimensional bodies invisible in one direction and three-dimensional bodies invisible in one and two orthogonal directions were constructed.
Keywords
Cite
@article{arxiv.1107.5667,
title = {Fractal bodies invisible in 2 and 3 directions},
author = {Alexander Plakhov and Vera Roshchina},
journal= {arXiv preprint arXiv:1107.5667},
year = {2011}
}