DYNAMICAL SYSTEMS Seminar

Thursday, December 3, 2020

Mixed random-quasiperiodic cocycles, Ⅰ: dynamics, ergodicity and consequences


Ao Cai
(CMAFCIO-FCUL)

Abstract: In 2018, Jiangong You raised a question asking what will be the behavior of the Lyapunov exponent for a random perturbation of the quasi-periodic Schrodinger cocycle. In this talk, we will introduce a more general and interesting model called mixed random-quasiperiodic cocycle that covers this special case. As a foundation of everything that follows (e.g. Furstenburg theory, uniform fiber LDT, regularity of the LE ), we will characterize the dynamics and study the ergodic properties of it in detail. As a consequence, we are able to obtain a uniform base LDT and a uniform fiber upper LDT in a very general setting. If time permits, we will also introduce a result of the next talks in advance and show how randomness dominates the quasi-periodicity in our context. This is a joint work with Pedro Duarte and Silvius Klein.

Thursday, December 3, 2020
Time: 11h00
Room: TBA
http://cemapre.iseg.ulisboa.pt/seminars/dynsys/