Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/21278
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dc.contributor.authorPlakhov, Alexanderpt
dc.contributor.authorTabachnikov, Sergeypt
dc.contributor.authorTreschev, Dmitrypt
dc.date.accessioned2017-12-22T10:43:29Z-
dc.date.available2017-12-22T10:43:29Z-
dc.date.issued2017-05-
dc.identifier.issn0393-0440pt
dc.identifier.urihttp://hdl.handle.net/10773/21278-
dc.description.abstractWe consider the following problem: given two parallel and identically oriented bundles of light rays in R^{n+1} and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We prove that a 2-mirror realization is possible, if and only if the diffeomorphism is the gradient of a function. We further prove that any orientation reversing diffeomorphism of domains in R^2 is locally the composition of two gradient diffeomorphisms, and therefore can be realized by 4 mirror reflections of light rays in R^3, while an orientation preserving diffeomorphism can be realized by 6 reflections. In general, we prove that an (orientation reversing or preserving) diffeomorphism of wave fronts of two normal families of light rays in R^3 can be realized by 6 or 7 reflections.pt
dc.language.isoengpt
dc.publisherElsevierpt
dc.relationinfo:eu-repo/grantAgreement/FCT/5876/147206/PTpt
dc.relationinfo:eu-repo/grantAgreement/FCT/5876-PPCDTI/113470/PTpt
dc.rightsopenAccesspor
dc.subjectBilliardspt
dc.subjectFreeform surfacespt
dc.subjectImagingpt
dc.subjectGeometrical opticspt
dc.titleBilliard transformations of parallel flows: a periscope theorempt
dc.typearticlept
dc.peerreviewedyespt
ua.distributioninternationalpt
degois.publication.firstPage157pt
degois.publication.lastPage166pt
degois.publication.titleJournal of Geometry and Physicspt
degois.publication.volume115pt
dc.identifier.doi10.1016/j.geomphys.2016.04.006pt
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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