Geodesic
A~universal measure for a~pencil of conics and the Great Poncelet Theorem
Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 613-632

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Borel measures on conics which are invariant under the Poncelet map are investigated. For a pencil of conics the existence of a universal measure, which is invariant with respect to each conic in the pencil, is proved. Using this measure a new proof of the Great Poncelet Theorem is given. A full description of invariant Borel measures is also presented. Bibliography: 10 titles.
Keywords: Great Poncelet Theorem, invariant measure, pencil of conics. 
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     author = {E. A. Avksentyev},
     title = {A~universal measure for a~pencil of conics and the {Great} {Poncelet} {Theorem}},
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E. A. Avksentyev. A~universal measure for a~pencil of conics and the Great Poncelet Theorem. Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 613-632. http://geodesic.mathdoc.fr/item/SM_2014_205_5_a0/