De‐Jun Feng

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math.DS2026

Dimensions of orthogonal projections of typical self-affine sets and measures

De-Jun Feng, Yu-Hao Xie

Let $T_{1}, \dots, T_{m}$ be a family of $d \times d$ invertible real matrices with $∥ T_{i} ∥ < 1/2$ for $1 \leq i \leq m$ . For $a = (a_{1}, \dots, a_{m}) \in R^{m d}$ , let $Ï^{\bf a}\…

math.DS2024

Dimension of homogeneous iterated function systems with algebraic translations

De-Jun Feng, Zhou Feng

Let $I^¼$ be the self-similar measure associated with a homogeneous iterated function system $I^¦ = {I^» x + t_{j}}_{j = 1}^{m}$ on $R$ and a probability vector $ (p_{j})_{j=1}^…