A Condition of Boshernitzan and Uniform Convergence in the Multiplicative Ergodic Theorem
Abstract
This paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts. If such a subshift satisfies a certain condition, originally introduced by Boshernitzan, every locally constant SL(2,R)valued cocycle is uniform. As a consequence, the corresponding Schrödinger operators exhibit Cantor spectrum of Lebesgue measure zero. An investigation of Boshernitzan's condition then shows that these results cover all earlier results of this type and, moreover, provide various new ones. In particular, Boshernitzan's condition is shown to hold for almost all circle maps and almost all ArnouxRauzy subshifts.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:math/0403190
 Bibcode:
 2004math......3190D
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematical Physics
 EPrint:
 38 pages