منابع مشابه
Zero Measure
We study the almost Mathieu operator: 1) + cos(2n +)u(n), on l 2 (Z), and show that for all ; , and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely j4 ? 2jjj. In particular, for jj = 2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and jj = 2) we show that the Hausdorr dimension of the spectrum is smaller than or equal to 1=2.
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For a subshift of finite type and a fixed Hölder continuous function, the zero measure invariant set of points where the Birkhoff averages do not exist is either empty or carries full Hausdorff dimension. Similar statements hold for conformal repellers and two-dimensional horseshoes, and the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05225-9