Speaker: Dr. Hisatoshi Yuasa, UNSW (Visiting Fellow)

Place: Red Centre, room 4082.
Date: the 13th of September.
Time: 12:00 -- 13:00.

Abstract:

A map from a finite alphabet to the set of nonempty words over the alphabet
is called a substitution. Since W. Gottschalk's work in 1963, the ergodic and
topological properties of the subshift arising from a primitive substitution
has been extensively studied by many authors.

In particular, it is well-known that the subshift is minimal and uniquely
ergodic. In this talk, a new class of non-primitive substitutions is introduced.
Those dynamical properties of the associated subshift are also discussed
which are the recurrence property called almost minimality and a uniqueness
in a certain sense of sigma-finite (not necessarily finite) invariant measures.

A key to the uniqueness of invariant measures is to represent the subshift
as an adic transformation, or a Bratteli-Vershik system.