TY - JOUR
T1 - Smale spaces from self-similar graph actions
AU - Yi, Inhyeop
N1 - Publisher Copyright:
Copyright © 2018 Rocky Mountain Mathematics Consortium.
PY - 2018
Y1 - 2018
N2 - We show that, for contracting and regular self-similar graph actions, the shift maps on limit spaces are positively expansive local homeomorphisms. From this, we find that limit solenoids of contracting and regular self- similar graph actions are Smale spaces and that the unstable Ruelle algebras of the limit solenoids are strongly Morita equivalent to the Cuntz-Pimsner algebras by Exel and Pardo if self-similar graph actions satisfy the contracting, regular, pseudo free and G-transitive conditions.
AB - We show that, for contracting and regular self-similar graph actions, the shift maps on limit spaces are positively expansive local homeomorphisms. From this, we find that limit solenoids of contracting and regular self- similar graph actions are Smale spaces and that the unstable Ruelle algebras of the limit solenoids are strongly Morita equivalent to the Cuntz-Pimsner algebras by Exel and Pardo if self-similar graph actions satisfy the contracting, regular, pseudo free and G-transitive conditions.
KW - Limit dynamical system
KW - Limit solenoid
KW - Positively expansive map
KW - Self-similar graph action
KW - Smale space
UR - http://www.scopus.com/inward/record.url?scp=85054572868&partnerID=8YFLogxK
U2 - 10.1216/RMJ-2018-48-4-1359
DO - 10.1216/RMJ-2018-48-4-1359
M3 - Article
AN - SCOPUS:85054572868
VL - 48
SP - 1359
EP - 1384
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
SN - 0035-7596
IS - 4
ER -