On SL(2,R) valued cocycles of hölder class with zero exponent over kronecker flows

Russell Johnson, Mahesh Nerurkar

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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 ! ∞.

Original languageEnglish (US)
Pages (from-to)873-884
Number of pages12
JournalCommunications on Pure and Applied Analysis
Volume10
Issue number3
DOIs
StatePublished - May 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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