Schreier graphs of the Basilica group
By D. D’Angeli, A. Donno, M. Matter, Tatiana Nagnibeda. 2009
69 citations recorded by the source corpus.
To any self-similar action of a finitely generated group $G$ of automorphisms of a regular rooted tree $T$ can be naturally associated an infinite sequence of finite graphs $\{\Gamma_n\}_{n\geq 1}$, where $\Gamma_n$ is the Schreier graph of the action of $G$ on the $n$-th level of $T$. Moreover, the action of $G$ on $\partial T$ gives rise to orbital Schreier graphs $\Gamma_{\xi}$, $\xi\in \partial T$. Denoting by $\xi_n$ the prefix of length $n$ of the infinite ray $\xi$, the rooted graph $(\Gamma_{\xi},\xi)$ is then the limit of the sequence of finite rooted graphs $\{(\Gamma_n,\xi_n)\}_{n\geq 1}$ in the sense of pointed Gromov-Hausdorff convergence. In this paper, we give a complete classification (up to isomorphism) of the limit graphs $(\Gamma_{\xi},\xi)$ associated with the Basilica group acting on the binary tree, in terms of the infinite binary sequence $\xi$.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ad63704bfe4f9a91c03517e96547e24404b2cc34
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In Applied Mathematics
In Mathematical Physics
- Volodymyr V. Nekrashevych
- Anatoly M. Vershik
- Enrique Pardo
- R. Exel
- Rostislav I. Grigorchuk
- A. Erschler
- Yaroslav Vorobets
- Mariya Vorobets
In Statistical and Nonlinear Physics
Citations in the corpus
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