Encontros IST-IME 

09/09/2022, 09:45 — 10:30 — Anfiteatro Abreu Faro
Pedro Duarte, Faculdade de Ciências, Universidade de Lisboa

Stability of the Lyapunov exponents of randomly perturbed quasi-periodic cocycles

The study of linear cocycles and their Lyapunov exponents in Ergodic Theory has an important interface with study of spectral properties of discrete Schrödinger operators in Mathematical Physics, namely via the regularity of the Lyapunov exponents of the Schrödinger cocycles which relate to the spectral properties of the associated Schrödinger operators. Many results have been obtained so far on the continuity of the Lyapunov exponents for two main classes of linear cocycles: the class of quasi-periodic linear cocycles and the class of random linear cocycles. In this talk, I will survey on recent work with Ao Cai and Silvius Klein on a problem posed by Jiangong You about the stability of the Lyapunov exponents for random perturbations of quasi-periodic Schrödinger cocycles.

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PedroDuarteISTIME22.pdf