MathSciDoc: An Archive for Mathematician ∫

 
Log In
Sign Up
Help
Go
 

Lq-spectrum of self-similar measures with overlaps in the absence of second-order identities

Sze-Man Ngai Hunnan Normal University and Georgia Southern University Yuanyuan Xie Hunan Normal University

Publications of CMSA of Harvard mathscidoc:1702.38001

For a self-similar measure in d-dimensional Euclidean space with overlaps but satisfies the so-called bounded measure type condition introduced by Tang and the authors, we set up a framework for deriving a closed formula for the Lq-spectrum of the measure for nonnegative q. The framework allows us to include iterated function systems that have different contraction ratios and those in higher dimension. For self-similar measures with overlaps, closed formulas for the Lq-spectrum have only been obtained earlier for measures satisfying Strichartz second-order identities. We illustrate how to use our results to prove the differentiability of the Lq-spectrum, obtain the multifractal dimension spectrum, and compute the Hausdorff dimension of the measure.
Fractal, Lq-spectrum, multifractal formalism, self-similar measures, bounded measure type condition
[ Download ] [ 2017-02-05 21:02:03 uploaded by smngai ] [ 1772 downloads ] [ 0 comments ] 
@inproceedings{sze-manlq-spectrum,
  title={Lq-spectrum of self-similar measures with overlaps in the absence of second-order identities},
  author={Sze-Man Ngai, and Yuanyuan Xie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205210203748078182},
}
Sze-Man Ngai, and Yuanyuan Xie. Lq-spectrum of self-similar measures with overlaps in the absence of second-order identities. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205210203748078182.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved