| Authors: | Dragović, Vladimir Radnović, Milena |
Affiliations: | Mechanics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Poncelet Porism in Singular Cases | Journal: | Regular and Chaotic Dynamics | Volume: | 30 | First page: | 598 | Last page: | 611 | Issue Date: | 2025 | Rank: | M22 | ISSN: | 1560-3547 | DOI: | 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 -gon inscribed in one of the conics and circumscribed about the other. |
Keywords: | Cayley’s conditions | Chebyshev polynomials | elliptic curves | geometry of conics | Poncelet theorem | singular cubics | Publisher: | Springer Link | Project: | 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. |
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