Definition:Variation of Function/Shift of Finite Type

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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:

$\map {\mathrm{var}_n} f := \sup \set {\size {\map f x - \map f y} : x, y \in X_\mathbf A, \; \forall i \in \openint {-n} n : x_i = y_i}$

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