The dimension of the non-dense orbit set for expanding maps
Dynamical Systems
2023-06-27 v1
Abstract
In this paper, we give a new proof for the Hausdorff dimension of the non-dense orbit set for expanding maps. This proof is based on the sharp lower bound of the Hausdorff dimension of repellers given by Cao, Pesin and Zhao in~\cite{caopesinzhao2019}. Besides, we prove that the Carathodory singular dimension of non-dense orbit set equals that of the repeller.
Keywords
Cite
@article{arxiv.2306.14621,
title = {The dimension of the non-dense orbit set for expanding maps},
author = {Congcong Qu},
journal= {arXiv preprint arXiv:2306.14621},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1906.07323 by other authors