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SUMMARY:Hans Koch (University of Texas at Austin\, USA)
DTSTART:20210202T150000Z
DTEND:20210202T160000Z
DTSTAMP:20260423T041111Z
UID:CRM-CAMP/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/29/
 ">Golden mean renormalization for the almost Mathieu operator and related 
 skew products</a>\nby Hans Koch (University of Texas at Austin\, USA) as p
 art of CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analy
 sis\n\n\nAbstract\nWe renormalize SL(2\,R) skew-product maps over circle r
 otations. Such maps arise e.g. in the spectral analysis of the Hofstadte
 r Hamiltonian and the almost Mathieu operator. For rotations by the inver
 se golden mean\, we prove the existence of two renormalization-periodic o
 rbits. We conjecture that there are infinitely many such orbits\, and th
 at the associated universal constants describe local scaling properties o
 f the Hofstadter spectrum and of the corresponding generalized eigenvecto
 rs. Some recent results on trigonometric skew-product maps will be descr
 ibed as well. This is joint work with Saša Kocić (UT Austin\, USA).\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/29/
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