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arXiv · 1603.06087

Connectedness of self-affine sets with product digit sets

Jing-Cheng Liu·Jun Jason Luo·Ke Tang
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Abstract

Let $T(A,\mathcal{D})$ be a self-affine set generated by an expanding matrix $A=\left[\begin{array}{rr} p & 0\cr -a & q \end{array}\right]$ and a product digit set $\mathcal{D}=\{0,1,\dots,m-1\}\times \{0,1,\dots,n-1\}$. We provide a necessary and sufficient condition for the $T(A,\mathcal{D})$ to be connected, which generalizes the known results.

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Jing-Cheng Liu, Jun Jason Luo, Ke Tang. 2016-03-19. Connectedness of self-affine sets with product digit sets. https://doi.org/10.1142/s0218348x17500530

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