38 citations · 90 across the 9 of their papers we have counts for
5 papers · 1 filter
Uniform positivity of the Lyapunov exponent for monotone potentials generated by the doubling map
Zhenghe Zhang
We show that for any doubling map generated monotone potential with derivative uniformly bounded away from zero, the Lyapunov exponent of the associated Schrödinger operators…
Cantor spectrum for a class of quasiperiodic Schrödinger operators
Yiqian Wang, Zhenghe Zhang
We show that for a class of quasiperiodic potentials and for any Diophantine frequency, the spectrum of the corresponding Schrödinger operators is Cantor. Our approach is of…
Uniform Positivity and Continuity of Lyapunov Exponents for a Class of Quasiperiodic Schrödinger Cocycles
Yiqian Wang, Zhenghe Zhang
We show that for a class of quasiperiodic potentials and for any Diophantine frequency, the Lyapunov exponents of the corresponding Schrödinger cocycles are uniformly positiv…
Uniform hyperbolicity and its relation with spectral analysis of 1D discrete Schrödinger Operators
Zhenghe Zhang
This paper intends to provide new, simple, and self-contained proofs of the equivalence of various different descriptions of the uniformly hyperbolic seq…
Positive Lyapunov Exponents for Quasiperiodic Szego cocycles
Zhenghe Zhang
In this paper we first obtain a formula of averaged Lyapunov exponents for ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using acceleration, we construct a class…