Authors: Dragović, Vladimir 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Poncelet-Darboux curves, their complete decomposition and Marden theorem
Journal: International Mathematics Research Notices
Volume: 2011
Issue: 15
First page: 3502
Last page: 3523
Issue Date: 8-Aug-2011
Rank: M21
ISSN: 1073-7928
DOI: 10.1093/imrn/rnq229
Poncelet-Darboux curves are studied. A Poncelet-Darboux curve of degree n-1 is completely decomposable if it consists of (n-1)/2 conics if n is odd; if n is even, completely decomposable curve consists of (n-2)/2 conics and a line. An effective criterion for complete decomposability in terms of pair of polynomials which defines a Poncelet-Darboux curve is derived. A relationship between Poncelet-Darboux curves and the Marden theorem from geometric theory of zeros of polynomial and rational functions is established.
Publisher: Oxford University Press
Project: Serbian Ministry of Science and Technology, Project Geometry and Topology of Manifolds and Integrable Dynamical Systems
Mathematical Physics Group of the University of Lisbon, Project Probabilistic approach to finite and infinite dimensional dynamical systems, PTDC/MAT/104173/2008

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