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arXiv · 1405.0781

Algorithms to test open set condition for self-similar set related to P.V. numbers

hao Li·qiu-li Guo·qin Wang·li-feng Xi
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Abstract

Fix a P.V. number $\lambda ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, $\mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}$, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda ^{p_{i}}E_{\mathbf{p},\mathbf{b}}+b_{i})$ we find an efficient algorithm to test whether $E_{\mathbf{p},\mathbf{b}}$ satisfies the open set condition (strong separation condition) or not.

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hao Li, qiu-li Guo, qin Wang, li-feng Xi. 2014-05-05. Algorithms to test open set condition for self-similar set related to P.V. numbers. https://arxiv.org/abs/1405.0781

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