- 04-75 David Damanik and Daniel Lenz
- A Condition of Boshernitzan and Uniform Convergence in the Multiplicative Ergodic Theorem
Mar 10, 04
(auto. generated ps),
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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 Schr\"odinger
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 Arnoux-Rauzy subshifts.