Schrödinger operators with potentials generated by hyperbolic transformations
Event details
| Date | 30.04.2021 |
| Hour | 16:15 |
| Speaker | Prof. David Damanik, Rice University |
| Location | Online |
| Category | Conferences - Seminars |
Please pay attention that it will unusually be held at 16:15
Abstract:
We discuss discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation and present results showing that the Lyapunov exponent is positive away from a small exceptional set of energies for suitable choices of the ergodic measure and the sampling function. These results apply in particular to Schrödinger operators defined over expanding maps on the unit circle, hyperbolic automorphisms of a finite-dimensional torus, and Markov chains. (Joint work with Artur Avila and Zhenghe Zhang)
Abstract:
We discuss discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation and present results showing that the Lyapunov exponent is positive away from a small exceptional set of energies for suitable choices of the ergodic measure and the sampling function. These results apply in particular to Schrödinger operators defined over expanding maps on the unit circle, hyperbolic automorphisms of a finite-dimensional torus, and Markov chains. (Joint work with Artur Avila and Zhenghe Zhang)
Practical information
- Informed public
- Free
Organizer
- Prof. Marius Lemm
Contact
- Nadia Kaiser