Geodesic
Properties of Lyapunov exponents for quasiperodic cocycles with singularities
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider the quasi-periodic cocycles $(\omega,A(x,E)): (x,v)\mapsto (x+\omega, A(x,E)v)$ with $\omega$ Diophantine. Let $M_2(\mathbb{C})$ be a normed space endowed with the matrix norm, whose elements are the $2\times 2$ matrices. Assume that $A:\mathbb{T}\times \mathcal{E}\to M_2(\mathbb{C})$ is jointly continuous, depends analytically on $x\in\mathbb{T}$ and is Holder continuous in $E\in\mathcal{E}$, where $\mathcal{E}$ is a compact metric space and $\mathbb{T}$ is the torus. We prove that if two Lyapunov exponents are distinct at one point $E_0\in\mathcal{E}$, then these two Lyapunov exponents are Holder continuous at any E in a ball central at $E_0$. Moreover, we will give the expressions of the radius of this ball and the Holder exponents of the two Lyapunov exponents.
Classification : 37C55, 37F10
Keywords: Lyapunov exponent, quasiperodic cocycles, holder exponent 
@article{EJDE_2015__2015__a28,
     author = {Tao, Kai},
     title = {Properties of {Lyapunov} exponents for quasiperodic cocycles with singularities},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a28/}
}
TY  - JOUR
AU  - Tao, Kai
TI  - Properties of Lyapunov exponents for quasiperodic cocycles with singularities
JO  - Electronic Journal of Differential Equations
PY  - 2015
VL  - 2015
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a28/
LA  - en
ID  - EJDE_2015__2015__a28
ER  - 
%0 Journal Article
%A Tao, Kai
%T Properties of Lyapunov exponents for quasiperodic cocycles with singularities
%J Electronic Journal of Differential Equations
%D 2015
%V 2015
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a28/
%G en
%F EJDE_2015__2015__a28
Tao, Kai. Properties of Lyapunov exponents for quasiperodic cocycles with singularities. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a28/