On fractal measures and diophantine approximation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On fractal measures and diophantine approximation

Authors:	Dmitry Kleinbock Elon Lindenstrauss Barak Weiss

Affiliation:	(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, Beer Sheva, Israel, 84105

Abstract:	We study diophantine properties of a typical point with respect to measures on $mathbb{R}^n .$ Namely, we identify geometric conditions on a measure on $mathbb{R}^n$ guaranteeing that -almost every ${bf y},in,mathbb{R}^n$ 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.

Keywords:	11J83
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