Definition:Variation of Function/Shift of Finite Type

Definition
Let $\struct {X _\mathbf A, \sigma_\mathbf A}$ be a shift of finite type.

Let $f : X _\mathbf A\to\C$ be a continuous function.

Let $n\in\N$.

The $n$th variation of $f$ is defined as:
 * $\map {\mathrm{var} _n} f := \sup \set { \size {f(x) - f(y)} : x,y\in X_\mathbf A, \;\forall i\in\openint {-n} n : x_i = y_i }$