2021/03/01 by Dragović, Vladimir, Radnović, Milena · 1 citation
#14H70 #34M55 #37A10 #37J70 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2103.01215
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∈\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.