Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910353514823680 |
|---|---|
| author | Dragović, Vladimir Radnović, Milena |
| author_facet | Dragović, Vladimir Radnović, Milena |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_01215 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil Dragović, Vladimir Radnović, Milena Dynamical Systems Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems 14H70, 37J70, 34M55, 37A10 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. |
| title | Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil |
| topic | Dynamical Systems Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems 14H70, 37J70, 34M55, 37A10 |
| url | https://arxiv.org/abs/2103.01215 |