On fractal measures and diophantine approximation |
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Authors: | Dmitry Kleinbock Elon Lindenstrauss and Barak Weiss |
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Institution: | (1) Brandeis University, Waltham, MA 02454-9110, USA;(2) Stanford University, Stanford, CA 94305, USA;(3) Present address: Princeton University, Princeton, NJ 08540, USA;(4) Ben Gurion University, Be er Sheva, Israel, 84105 |
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Abstract: | We study diophantine properties of a typical point with respect to measures on
Namely, we identify geometric conditions on a measure on
guaranteeing that -almost every
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 main result of KM]. Another class of examples is given by measures supported on self-similar sets satisfying the open set condition, as well as their products and pushforwards by certain smooth maps. |
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Keywords: | 11J83 |
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