Authors: Dragović, Vladimir 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Dynamics of extremal polynomials, Painleve VI equations, and isoharmonic deformations
First page: 16
Conference: Mathematics and Applications, 11th Symposium, Mathematics Faculty, Belgrade, 3-4 December 2021
Issue Date: 2021
Rank: M32
URL: http://alas.matf.bg.ac.rs/~konferencija/KNJIGA_APSTRAKATA_2021.pdf
Abstract: 
The talk is based on interrelations between integrable billiards, extremal polynomials, Riemann
surfaces, potential theory, and isomonodromic deformations. We discuss injectivity properties of rotation and winding numbers. We study dynamics of Chebyshev polynomials on several intervals and introduce a notion of isoharmonic deformations. We study their isomonodromic properties and formulate a new class of constrained Schlesinger systems. We provide explicit solutions to these systems. The talk is based on joint results with Vasilisa Shramchenko, including work in progress.
Publisher: University of Belgrade, Faculty of Mathematics

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