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Session II.1 - Computational Dynamics

Saturday, June 17, 17:00 ~ 17:30

Asymptotic scaling and universality for skew products with factors in SL(2,R)

Hans Koch

The Universiy of Texas at Austin, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider the asymptotic properties of matrix products that appear in the study of the Hofstadter model (of an electron moving on a lattice) and the associated almost Mathieu operators. In a restricted setup that is characterized by a symmetry, we show that critical behavior occurs and is universal in an open neighborhood of the almost Mathieu family. This behavior is governed by a periodic orbit of a renormalization transformation. Other periodic orbits govern supercritical behavior.

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