Poncelet Porism in Singular Cases

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI:10.1134/S1560354725040094

Vladimir Dragović, Milena Radnović

引用次数: 0

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.

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奇异情况下的庞塞莱波律

著名的庞塞勒波率通常是研究一对处于一般位置的光滑圆锥曲线。这里我们讨论了真实平面上的庞塞勒波度——仿射或射影，当不存在这种情况时，即，圆锥曲线至少有一个切点或至少有一个圆锥曲线是不光滑的。在所有这些情况下，我们都找到了一条\(n\) -曲线存在的充分必要条件，这条曲线内嵌在其中一条曲线上，并以另一条曲线为界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.