University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Continuity of Lyapunov Exponents and Cantor spectrum for a class of $C^2$ Quasiperiodic Schr"odinger Cocycles

Continuity of Lyapunov Exponents and Cantor spectrum for a class of $C^2$ Quasiperiodic Schr"odinger Cocycles

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Periodic and Ergodic Spectral Problems

Co-author: Zhenghe Zhang (Rice University)

We show that for a class of $C^2$ quasiperiodic potentials and for any fixed mph{Diophantine} frequency, the Lyapunov exponents of the corresponding Schr”odinger cocycles are uniformly positive and weakly H”older continuous as function of energies. Moreover, we show that the spectrum is Cantor. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to general quasiperiodic $mathrm{SL}(2,R)$ cocycles.

This talk is part of the Isaac Newton Institute Seminar Series series.

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