L. Golinskii
Published 2005-11-10, updated 2006-01-14Version 2
The relation between the Toda lattices and similar nonlinear chains and orthogonal polynomials on the real line has been elaborated immensely for the last decades. We examine another system of the differential-difference equations known as the Schur flow within the framework of the theory of orthogonal polynomials on the unit circle. This system can be exhibited in equivalent form as the Lax equation, and the corresponding spectral measure undergoes a simple transformation. The general result is illustrated on the modified Bessel measures on the unit circle and the long time behavior of their Verblunsky coefficients.
Comments: 17 pages, section 4 revised essentially
Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlevé equations
Orthogonal Polynomials
A note on Poisson brackets for orthogonal polynomials on the unit circle
![QR code for arXiv:math/0511269 [math.CA]](http://oss.arxitics.com/images/favicon.svg)