Diophantine approximation and self-conformal measures
نویسندگان
چکیده
منابع مشابه
On Fractal Measures and Diophantine Approximation
We study diophantine properties of a typical point with respect to measures on Rn. Namely, we identify geometric conditions on a measure μ on Rn guaranteeing that μ-almost every y ∈ Rn is not very well multiplicatively approximable by rationals. Measures satisfying our conditions are called ‘friendly’. Examples include smooth measures on nondegenerate manifolds; thus this paper generalizes the ...
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Let W (ψ) denote the set of ψ-well approximable points in Rd and let K be a compact subset of Rd which supports a measure μ. In this short note, we show that if μ is an ‘absolutely friendly’ measure and a certain μ–volume sum converges then μ(W (ψ) ∩K) = 0. The result obtained is in some sense analogous to the convergence part of Khintchines classical theorem in the theory of metric Diophantine...
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The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2005
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.07.004