Alexei Poltoratski, Christian Remling
Reflectionless Herglotz functions and generalized Lyapunov exponents
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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 general setting. This is related to the previous 
material because the density of states measures are reflectionless on certain sets.