We prove uniform positivity of the Lyapunov exponent for quasiperiodic SchrSdinger cocycles with C2 cos-type potentials, large coupling constants, and fixed weak Liouville frequencies.
We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a C2 cos-type potential and a weak Liouville frequency.We propose a new method to prove that the Lyapunov exp...We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a C2 cos-type potential and a weak Liouville frequency.We propose a new method to prove that the Lyapunov exponent is continuous in energies.In particular,a large deviation theorem is not needed in the proof.展开更多
We prove the joint continuity of Lyapunov exponent in the energy and the Diophantine frequency for quasi-periodic Schrodinger cocycles with the C^(2)cos-type potentials.In particular,the Lyapunov exponent is log-Holde...We prove the joint continuity of Lyapunov exponent in the energy and the Diophantine frequency for quasi-periodic Schrodinger cocycles with the C^(2)cos-type potentials.In particular,the Lyapunov exponent is log-Holder continuous at each Diophantine frequency.展开更多
文摘We prove uniform positivity of the Lyapunov exponent for quasiperiodic SchrSdinger cocycles with C2 cos-type potentials, large coupling constants, and fixed weak Liouville frequencies.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11771205).
文摘We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a C2 cos-type potential and a weak Liouville frequency.We propose a new method to prove that the Lyapunov exponent is continuous in energies.In particular,a large deviation theorem is not needed in the proof.
文摘We prove the joint continuity of Lyapunov exponent in the energy and the Diophantine frequency for quasi-periodic Schrodinger cocycles with the C^(2)cos-type potentials.In particular,the Lyapunov exponent is log-Holder continuous at each Diophantine frequency.
