On fractal measures and diophantine approximation View Full Text


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Article Info

DATE

2005-04

AUTHORS

Dmitry Kleinbock, Elon Lindenstrauss, Barak Weiss

ABSTRACT

We study diophantine properties of a typical point with respect to measures on Namely, we identify geometric conditions on a measure μ on guaranteeing that μ-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. More... »

PAGES

479

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00029-004-0378-2

DOI

http://dx.doi.org/10.1007/s00029-004-0378-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1042724018


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