Reflectionless Herglotz functions and generalized Lyapunov exponents
Spectral Theory
2008-05-30 v1 Mathematical Physics
Complex Variables
math.MP
Abstract
We study several related aspects of reflectionless Jacobi matrices. Our first set of results deals with the singular part of reflectionless measures. We then introduce and discuss Lyapunov exponents, density of states measures, and other related quantities in a \textit{general} setting. This is related to the previous material because the density of states measures are reflectionless on certain sets.
Cite
@article{arxiv.0805.4439,
title = {Reflectionless Herglotz functions and generalized Lyapunov exponents},
author = {Alexei Poltoratski and Christian Remling},
journal= {arXiv preprint arXiv:0805.4439},
year = {2008}
}