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

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.

References in corpus (2)

• Lipschitz equivalence of self-similar sets and hyperbolic boundaries
• Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem