Some dimensional results for homogeneous Moran sets

Abstract

Let M ({ nk } k ≥1,{ ck }k≥1) be the collection of homogeneous Moran sets determined by { n k}k≥1and { ck }k≥1, where { nk }k≥1 is a sequence of positive integers and { ck }k≥1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in M are determined. The result is proved that for any value s between the maximal and minimal values, there exists an element in M { nk } k ≥1, { ck } k ≥1) such that its Hausdorff dimension is equal to s. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.