Open AccessSchreier graphs of the Basilica group
Author(s) -
Daniele D’Angeli,
Alfredo Donno,
Michel Matter,
Tatiagnibeda
Publication year - 2010
Publication title -
journal of modern dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.668
H-Index - 25
eISSN - 1930-532X
pISSN - 1930-5311
DOI - 10.3934/jmd.2010.4.167
Subject(s) - mathematics , combinatorics , isomorphism (crystallography) , sequence (biology) , tree (set theory) , prefix , group (periodic table) , hausdorff space , limit (mathematics) , limit of a sequence , binary tree , discrete mathematics , mathematical analysis , chemistry , organic chemistry , linguistics , philosophy , biology , crystal structure , genetics , crystallography
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 >= 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 derivative T gives rise to orbital Schreier graphs Gamma(xi), xi is an element of partial derivative 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 >= 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