从共焦点铅笔看刻画在圆内和圆锥周边的庞塞莱多边形的等周期族

IF 0.5 4区数学 Q3 MATHEMATICS Geometriae Dedicata Pub Date : 2024-05-14 DOI:10.1007/s10711-024-00929-9

Vladimir Dragović, Milena Radnović

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引用次数: 0

摘要

在数值范围和布拉什克积的分析中，自然会出现内切于圆并以共焦系圆锥为圆心的庞塞莱多边形。我们研究了当内切圆锥通过共焦笔变化时这种多边形的行为，并发现了当来自共焦族的每个圆锥都内切于一个具有相同 n 的 n-polygon 时的情形。我们建立了庞斯莱四边形和六边形族与 Painlevé VI 方程的解之间的关系。

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Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil

Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal family naturally arise in the analysis of the numerical range and Blaschke products. We examine the behaviour of such polygons when the inscribed conic varies through a confocal pencil and discover cases when each conic from the confocal family is inscribed in an n-polygon, which is inscribed in the circle, with the same n. Complete geometric characterization of such cases for $n\in \{4,6\}$ is given and proved that this cannot happen for other values of n. We establish a relationship of such families of Poncelet quadrangles and hexagons to solutions of a Painlevé VI equation.

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.

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