Fractal bodies invisible in 2 and 3 directions

Alexander Plakhov; Vera Roshchina

doi:10.3934/dcds.2013.33.1615

Article Contents

2013, Volume 33, Issue 4: 1615-1631. Doi: 10.3934/dcds.2013.33.1615

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Fractal bodies invisible in 2 and 3 directions

Alexander Plakhov^1, and
Vera Roshchina^2,

1.
Department of Mathematics, University of Aveiro, Aveiro 3810-193
2.
Collaborative Research Network, University of Ballarat, VIC 3353

Received: October 2011

Revised: January 2012

Published: April 2013

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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 [1,12], where two-dimensional bodies invisible in one direction and three-dimensional bodies invisible in one and two orthogonal directions were constructed.

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Mathematics Subject Classification: Primary: 78A05, 37D50; Secondary: 76G25.

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References

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