English

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 Caratheˊ\acute{\text{e}}odory 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