A Condition of Boshernitzan and Uniform Convergence in the Multiplicative Ergodic Theorem

Details A Condition of Boshernitzan and Uniform Convergence in the Multiplicative Ergodic Theorem A Condition of Boshernitzan and Uniform Convergence in the Multiplicative Ergodic Theorem

2004-03-11

arxiv.org/abs/math/0403190v1

Mathematics

Dynamical Systems

38 pages

Scientific paper

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.

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