Manfred Denker: Toral Automorphisms Driven by Continued Fractions

Explore a 57-minute lecture on toral automorphisms driven by continued fractions, presented by Manfred Denker at the Hausdorff Center for Mathematics. Delve into the mathematical concepts surrounding two irrational numbers α+ and α− and their role in defining a sequence of toral automorphisms. Examine the 'quenched' Poisson limit of these sequences, utilizing Chen's approach and moving beyond traditional transfer operator methods. Investigate the use of homoclinic groups and Steiner's theorem in determining set geometry. Follow the lecture's progression through topics such as continued fraction expansions, mutations, exceptional points, exponential goals, and interference methods. Gain insights into this collaborative work with the late M. Gordin, presented as part of the Hausdorff Trimester Program "Dynamics: Topology and Numbers" conference on transfer operators in number theory and quantum chaos.

Intro
Setup
Continued fraction expansion
Mutations
Exceptional points
Exponential goal
Genocide method
Interference method