Damanik, David2019-05-172019-05-172018-052018-04-02May 2018VandenBoom, Tom. "Isospectral dynamics of reflectionless Jacobi operators." (2018) Diss., Rice University. <a href="https://hdl.handle.net/1911/105699">https://hdl.handle.net/1911/105699</a>.https://hdl.handle.net/1911/105699This thesis focuses on the isospectral torus of reflectionless Jacobi operators and the dynamics of its automorphisms. The novel perspective which it hopes to advertise is one of the joint utility of inverse spectral theoretic techniques and dynamical techniques to address direct and inverse spectral problems, respectively. Concretely, we use the former perspective to prove the reducibility of the shift cocycle for certain reflectionless Jacobi operators, and we use the latter perspective to prove spectral atypicality of discrete Schroedinger operators.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Mathematical physicsJacobi operatorsdynamical systemsinverse spectral theoryThesis2019-05-17