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Regular and Chaotic Dynamics, 2025, Volume 30, Issue 4, Pages 598–611
DOI: https://doi.org/10.1134/S1560354725040094 (Mi rcd1323) 		 
Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

Poncelet Porism in Singular Cases

Vladimir Dragovićab, Milena Radnovićca

a Mathematical Institute SANU, Belgrade, Kneza Mihaila 36, 11000 Belgrade, Serbia
b The University of Texas at Dallas, Department of Mathematical Sciences, 800 W. Campbell Rd, 75080-3021 Richardson TX, USA
c The University of Sydney, School of Mathematics and Statistics, Carslaw F07, 2006 NSW, Australia
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DOI: https://doi.org/10.1134/S1560354725040094
Abstract: The celebrated Poncelet porism is usually studied for a pair of smooth conics that are in a general position. Here we discuss Poncelet porism in the real plane — affine or projective, when that is not the case, i. e., the conics have at least one point of tangency or at least one of the conics is not smooth. In all such cases, we find necessary and sufficient conditions for the existence of an $n$-gon inscribed in one of the conics and circumscribed about the other.
Keywords: Poncelet theorem, Cayley’s conditions, geometry of conics, elliptic curves, singular cubics, Chebyshev polynomials
Funding agency Grant number
Australian Research Council 190101838
Simons Foundation 854861
This research was supported by the Australian Research Council, Discovery Project 190101838 Billiards within quadrics and beyond, the Serbian Ministry of Science, Technological Development and Innovation and the Science Fund of Serbia grant IntegraRS, and the Simons Foundation grant no. 854861.
Received: 30.04.2025
Accepted: 04.07.2025
Document Type: Article
MSC: 51N15, 14H70
Language: English
Citation: Vladimir Dragović, Milena Radnović, “Poncelet Porism in Singular Cases”, Regul. Chaotic Dyn., 30:4 (2025), 598–611
Citation in format AMSBIB
\Bibitem{DraRad25}
\by Vladimir Dragovi\'c, Milena Radnovi\'c
\paper Poncelet Porism in Singular Cases
\jour Regul. Chaotic Dyn.
\yr 2025
\vol 30
\issue 4
\pages 598--611
\mathnet{http://mi.mathnet.ru/rcd1323}
\crossref{https://doi.org/10.1134/S1560354725040094}
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