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Sbornik: Mathematics, 2014, Volume 205, Issue 5, Pages 613–632
DOI: https://doi.org/10.1070/SM2014v205n05ABEH004390 (Mi sm8203) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A universal measure for a pencil of conics and the Great Poncelet Theorem

E. A. Avksentyev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (572 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2014v205n05ABEH004390
Abstract: 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.
Received: 22.12.2012 and 09.11.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 5, Pages 3–22
DOI: https://doi.org/10.4213/sm8203
Bibliographic databases:
Document Type: Article
UDC: 514.144.2
MSC: 51N15
Language: English
Original paper language: Russian
Citation: E. A. Avksentyev, “A universal measure for a pencil of conics and the Great Poncelet Theorem”, Mat. Sb., 205:5 (2014), 3–22; Sb. Math., 205:5 (2014), 613–632
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v205/i5/p3
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:534
    Russian version PDF:279
    English version PDF:7
    References:55
    First page:39
     
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