One-Dimensional Ergodic Schrodinger Operators
II. Specific Classes

David Damanik (Author), Jake Fillman (Author)

9781470479244

Paperback / softback, published 28 February 2025

627 pages
25.4 x 17.8 x 3.7 cm, 1.1 kg

The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. The current volume addresses specific classes of operators, including the important examples of random and almost-periodic operators. The text serves as a self-contained introduction to the field for junior researchers and beginning graduate students, as well as a reference text for people already working in this area. The general theory of one-dimensional ergodic operators was presented in the book by the same authors as volume 221 in the Graduate Studies in Mathematics series.

• Highlights from Part I
• Part II: Specific classes
• Random potentials
• Almost-periodic potentials
• Periodic potentials
• Limit-periodic potentials
• Quasi-periodic potentials
• Subshift potentials
• Appendices
• Continued fractions
• Topological groups
• A crash course in combinatorial word theory
• List of open problems
• Glossary of notation
• Bibliography
• Index