Continuous Spectrum or Measurable Reducibility for Quasiperiodic Cocycles in {T ^{d} × SU(2)}
Abstract
We continue our study of the local theory for quasiperiodic cocycles in {T ^{d} × G} , where {G=SU(2)} , over a rotation satisfying a Diophantine condition and satisfying a closenesstoconstants condition, by proving a dichotomy between measurable reducibility (and therefore pure point spectrum), and purely continuous spectrum in the space orthogonal to {L^{2}(T ^{d}) \hookrightarrow L^{2}(T ^{d} × G)} . Subsequently, we describe the equivalence classes of cocycles under smooth conjugacy, as a function of the parameters defining their K.A.M. normal form. Finally, we derive a complete classification of the dynamics of onefrequency ( d = 1) cocycles over a recurrent Diophantine rotation.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 March 2018
 DOI:
 10.1007/s0022001730343
 arXiv:
 arXiv:1512.00057
 Bibcode:
 2018CMaPh.358..741K
 Keywords:

 Mathematics  Dynamical Systems;
 37C55;
 37A30
 EPrint:
 25 pages, 1 figure. arXiv admin note: text overlap with arXiv:1407.4763