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

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. (paper)
Authors:
 [1]
  1. Faculty of Mechanics and Mathematics, Moscow State University (Russian Federation)
Publication Date:
OSTI Identifier:
22365150
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 5; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; MEASURE THEORY