TY - JOUR
T1 - On SL(2,R) valued cocycles of hölder class with zero exponent over kronecker flows
AU - Johnson, Russell
AU - Nerurkar, Mahesh
PY - 2011/5
Y1 - 2011/5
N2 - We show that a generic SL(2,R) valued cocycle in the class of C r,(0 < r < 1) cocycles based on a rotation ow on the d-torus, is either uniformly hyperbolic or has zero Lyapunov exponents provided that the components of winding vector γ̄ = (γ1, ⋯ ,γd) of the rotation ow are rationally independent and satisfy the following super Liouvillian condition : |γi-p in/qn|≤Ce-q1+δn , 1≤i≤d , nε N , where C > 0 and δ > 0 are some constants and pin , qn are some sequences of integers with qn ! ∞.
AB - We show that a generic SL(2,R) valued cocycle in the class of C r,(0 < r < 1) cocycles based on a rotation ow on the d-torus, is either uniformly hyperbolic or has zero Lyapunov exponents provided that the components of winding vector γ̄ = (γ1, ⋯ ,γd) of the rotation ow are rationally independent and satisfy the following super Liouvillian condition : |γi-p in/qn|≤Ce-q1+δn , 1≤i≤d , nε N , where C > 0 and δ > 0 are some constants and pin , qn are some sequences of integers with qn ! ∞.
UR - http://www.scopus.com/inward/record.url?scp=80053052426&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80053052426&partnerID=8YFLogxK
U2 - 10.3934/cpaa.2011.10.873
DO - 10.3934/cpaa.2011.10.873
M3 - Article
SN - 1534-0392
VL - 10
SP - 873
EP - 884
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 3
ER -