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Cai-Yun Ma

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Preprint Oct 2026

Random Survivor Sets with Moving Holes in Bedford-McMullen Carpets

Let $2\le m<n$ be integers, and let $K(\mathcal{A})$ be the Bedford--McMullen carpet generated by $\{(x,y)\mapsto((x+i)/m,(y+j)/n):(i,j)\in\mathcal{A}\}$, where $\mathcal{A}$ is a subset of $\{0,1,\ldots,m-1\}\times\{0,1,\ldots,n-1\}$. Write $\mathcal{B}$ for the set of occupied columns, and assume that $\#\mathcal{B}\...

De-Rong Kong, Cai-Yun Ma, K. Simon · 0 citations

Preprint Sep 2026

Separation Conditions for Iterated Function Systems with a Common Attractor

Let $K$ be the non-singleton attractor of a finite iterated function system $\Phi=\{\phi_i(x)=a_i O_i x+t_i\}_{i=1}^m$ on $\mathbb{R}^d$, where $0<a_i<1$, $t_i\in\mathbb{R}^d$ and the $O_i$ are orthogonal transformations on $\mathbb{R}^d$. Suppose that $\Phi$ satisfies the open set condition, but not the strong separat...

Cai-Yun Ma · 0 citations