Volume no :20, Issue no: 1, February (2019)

Journal of Pure and Applied Mathematics: Advances and Applications

MULTIFRACTAL ANALYSIS ON THE DIVERGENCE SET OF ASYMPTOTICALLY ADDITIVE SEQUENCE

Author's: Guan-Zhong Ma and Gui-Xia Yuan
Pages: [41] - [60]
Received Date: December 16, 2018
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100122027

Abstract

Authors consider the Hausdorff dimension of the divergence set for asymptotically additive sequence in a class of non-uniformly expanding systems. Using techniques of constructing “Moran set” and joining n-level Bernoulli measures, they prove that the Hausdorff dimension of the divergence set in this class of systems has “dichotomy”, i.e., if the divergence set is not empty set, it will has full Hausdorff dimension.

Keywords

divergence set, Moran set, non-uniformly expanding systems.