Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 67, pp. 116.
Properties of Lyapunov exponents for quasiperodic cocycles with singularities
Kai Tao
Abstract:
We consider the quasiperiodic cocycles
with
Diophantine. Let
be a normed space endowed with the
matrix norm, whose elements are the
matrices.
Assume that
is jointly continuous,
depends analytically on
and is Holder continuous in
,
where
is a compact metric space and
is the torus. We prove that if two Lyapunov
exponents are distinct at one point
,
then these two
Lyapunov exponents are Holder continuous at any E in a ball
central at
.
Moreover, we will give the expressions of the radius
of this ball and the Holder exponents of the two Lyapunov exponents.
Submitted October 10, 2014. Published March 20, 2015.
Math Subject Classifications: 37C55, 37F10.
Key Words: Lyapunov exponent; quasiperodic cocycles; Holder exponent.
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Kai Tao
College of Sciences, Hohai University
1 Xikang Road
Nanjing, Jiangsu 210098, China
email: ktao@hhu.edu.cn, tao.nju@gmail.com

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