Define a continuous map ('the shift') on X by
Then is a dynamical system. More generally we shall consider a closed
-invariant subset XA determined by an
-matrix A = (Aij) with entries from
in the following way:
Since ,
is a dynamical system known as a one-sided subshift of finite type. In the course we shall study such systems and in particular obtain necessary and sufficient conditions for two one-sided subshifts of finite type to be conjugate. (Two dynamical systems
and
are conjugate when there is a homeomorphism
such that
.)
We will also consider two-sided subshifts of finite type which are defined similarly from bi-infinite sequence and address the same questions for these.
Qualifications
Geometry 1, Analysis 1.
Textbook
Bruce P. Kitchens: Symbolic Dynamics, Springer Verlag, Berlin 1997.