Reflectionless Herglotz functions and generalized Lyapunov exponents
  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. 
Alexei Poltoratski and Christian Remling