Abstract: This presentation examines the ergodic and dynamical properties of symbolic dynamical systems generated by substitutions on infinite countable alphabets. While the theory for finite alphabets is well-established, the countable setting presents unique challenges and remains less explored. The analysis centers on shift dynamical systems associated with irreducible substitutions, extending classical results to the infinite case. By investigating the dynamical behavior of the countable integer matrix inherent to the substitution, this talk establishes criteria for the existence and uniqueness of shift-invariant measures.

 

Organizer: Jung-Chao Ban (NCCU)