Metric relations in groups of tree automorphisms

1998 ◽  
Vol 37 (3) ◽  
pp. 192-203
Author(s):  
A. V. Rozhkov
Keyword(s):  
Tree Automorphisms

scholarly journals FINITELY CONSTRAINED GROUPS OF MAXIMAL HAUSDORFF DIMENSION

2015 ◽  
Vol 100 (1) ◽  
pp. 108-123 ◽  
Author(s):  
ANDREW PENLAND ◽  
ZORAN ŠUNIĆ
Keyword(s):  
Hausdorff Dimension ◽  
Finite Type ◽  
Binary Tree ◽  
Rooted Tree ◽  
Finitely Generated ◽  
Subshift Of Finite Type ◽  
Regular Tree ◽  
Pattern Size ◽  
Tree Automorphisms ◽  
Pattern Group

We prove that if $G_{P}$ is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group $P$ of pattern size $d$, $d\geq 2$, and if $G_{P}$ has maximal Hausdorff dimension (equal to $1-1/2^{d-1}$), then $G_{P}$ is not topologically finitely generated. We describe precisely all essential pattern groups $P$ that yield finitely constrained groups with maximal Hausdorff dimension. For a given size $d$, $d\geq 2$, there are exactly $2^{d-1}$ such pattern groups and they are all maximal in the group of automorphisms of the finite rooted regular tree of depth $d$.

scholarly journals ON THE WORD AND PERIOD GROWTH OF SOME GROUPS OF TREE AUTOMORPHISMS

2001 ◽  
Vol 29 (11) ◽  
pp. 4923-4964 ◽  
Author(s):  
Laurent Bartholdi ◽  
Zoran S˘unik´
Keyword(s):  
Tree Automorphisms
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