The dimension of the non-dense orbit set for expanding maps
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~caopesinzhao2019. Besides, we prove that the Caratheodory singular dimension of non-dense orbit set equals that of the repeller.
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