Nonsmooth Convex Caustics for Birkhoff Billiards

dc.contributor.ORCID0000-0002-4500-8394 (Arnold, M)
dc.contributor.authorArnold, Maxim
dc.contributor.authorBialy, Misha
dc.contributor.utdAuthorArnold, Maxim
dc.date.accessioned2019-05-31T22:21:15Z
dc.date.available2019-05-31T22:21:15Z
dc.date.created2018-04-11
dc.descriptionFull text access from Treasures at UT Dallas is restricted to current UTD affiliates.
dc.description.abstractThis paper is devoted to the examination of the properties of the string construction for the Birkhoff billiard. Based on purely geometric considerations, string construction is suited to providing a table for the Birkhoff billiard, having the prescribed caustic. Exploiting this framework together with the properties of convex caustics, we give a geometric proof of a result by Innami first proved in 2002 by means of Aubry-Mather theory. In the second part of the paper we show that applying the string construction one can find a new collection of examples of C-2-smooth convex billiard tables with a nonsmooth convex caustic.
dc.identifier.bibliographicCitationArnold, Maxim, and Misha Bialy. 2018. "Nonsmooth convex caustics for birkhoff billiards." Pacific Journal of Mathematics 295(2), doi: 10.2140/pjm.2018.295.257
dc.identifier.issn0030-8730
dc.identifier.issue2
dc.identifier.urihttps://hdl.handle.net/10735.1/6545
dc.identifier.volume295
dc.language.isoen
dc.publisherMathematical Sciences Publishers
dc.relation.urihttp://dx.doi.org/10.2140/pjm.2018.295.257
dc.rights©2018 Mathematical Sciences Publishers
dc.source.journalPacific Journal of Mathematics
dc.subjectMathematics
dc.subjectCaustics (Optics)
dc.titleNonsmooth Convex Caustics for Birkhoff Billiards
dc.type.genrearticle

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