ncku-talk2010-08-13

NCTS(South) Seminar

DATE 2010-08-13　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Prof. Yiqian Wang (王奕倩教授)（南京大學數學系）

TITLE Regularity of the Lyapunov exponent for quasi-periodic cocycles

ABSTRACT Lyapunov exponent is one of the critical concepts in the study of quasi-periodic cocycles. Many properties of quasi-periodic cocycles, such as hyperbolicity, reducibility as well as the spectrum of Schrodinger operators heavily depend on the knowledge of Lyapunov exponent.
In this talk, we first survey results on regularity of the Lyapunov exponent for analytic quasi-periodic cocycles, which plays a key role in solving the famous "Ten Martini Problems" on Almost Mathieu operator. Then we will introduce advances on continuity of the Lyapunov exponent for non-analytic quasi-periodic cocycles.

NCTS(South) Seminar

DATE	2010-08-13　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Prof. Yiqian Wang (王奕倩教授)（南京大學數學系）

TITLE	Regularity of the Lyapunov exponent for quasi-periodic cocycles

ABSTRACT	Lyapunov exponent is one of the critical concepts in the study of quasi-periodic cocycles. Many properties of quasi-periodic cocycles, such as hyperbolicity, reducibility as well as the spectrum of Schrodinger operators heavily depend on the knowledge of Lyapunov exponent. In this talk, we first survey results on regularity of the Lyapunov exponent for analytic quasi-periodic cocycles, which plays a key role in solving the famous "Ten Martini Problems" on Almost Mathieu operator. Then we will introduce advances on continuity of the Lyapunov exponent for non-analytic quasi-periodic cocycles.