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Heterogeneous ubiquitous systems in ℝ d and Hausdorff dimension

Heterogeneous ubiquitous systems in ℝ d and Hausdorff dimension Let {x n } n∈ℕ be a sequence in [0, 1] d , {λ n }n∈ℕ a sequence of positive real numbers converging to 0, and δ > 1. The classical ubiquity results are concerned with the computation of the Hausdorff dimension of limsup-sets of the form $$ S{\left( \delta \right)} = {\bigcap\limits_{N \in \mathbb{N}} \; {{\bigcup\limits_{n \geqslant N} {B{\left( {x_{n} ,\lambda ^{\delta }_{n} } \right)}} }} }. $$ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Heterogeneous ubiquitous systems in ℝ d and Hausdorff dimension

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References (64)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-007-0056-z
Publisher site
See Article on Publisher Site

Abstract

Let {x n } n∈ℕ be a sequence in [0, 1] d , {λ n }n∈ℕ a sequence of positive real numbers converging to 0, and δ > 1. The classical ubiquity results are concerned with the computation of the Hausdorff dimension of limsup-sets of the form $$ S{\left( \delta \right)} = {\bigcap\limits_{N \in \mathbb{N}} \; {{\bigcup\limits_{n \geqslant N} {B{\left( {x_{n} ,\lambda ^{\delta }_{n} } \right)}} }} }. $$

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Jan 1, 2007

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