Universal measure for Poncelet-type theorems

Avksentyev, Evgeny; Protasov, Vladimir

doi:10.1090/proc/13838

Universal measure for Poncelet-type theorems

Authors: Evgeny A. Avksentyev and Vladimir Yu. Protasov
Journal: Proc. Amer. Math. Soc. 146 (2018), 4843-4854
MSC (2010): Primary 53A04, 28A25, 51N15
DOI: https://doi.org/10.1090/proc/13838
Published electronically: August 10, 2018
MathSciNet review: 3856151
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Abstract: We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measure are well known and have been used in the literature to prove Poncelet's and the zigzag theorems. Some further generalizations are also obtained by applying the new measure.

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