### Renormalization for the almost Mathieu operator and related skew products.

- Series
- CDSNS Colloquium
- Time
- Friday, November 1, 2019 - 11:15 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Hans Koch – Univ. of Texas, Austin – koch@math.utexas.edu

Considering SL(2,R) skew-product maps over circle rotations,

we prove that a renormalization transformation

associated with the golden mean alpha

has a nontrivial periodic orbit of length 3.

We also present some numerical results,

including evidence that this period 3 describes

scaling properties of the Hofstadter butterfly

near the top of the spectrum at alpha,

and scaling properties of the generalized eigenfunction

for this energy.