Finite setting Sample Clauses

Finite setting. The thermodynamic formalism for H¨older continuous potentials on a subshift of finite type is well understood and a detailed account can be found in [PP]. However, in this thesis the amount of results required from this setting is limited to knowing about the existence of Xxxxx measures and their characterisation. Therefore, these are the only results we present here, all of which can be found in [PP]. Let A be an aperiodic matrix and (Σ, σ) be its associated subshift of finite type. For a continuous function f : Σ → C and n “ 1 we define xxxx(f ) = sup{|f (i) − f (j)| : i|m = j|m for m < n} to be the nth variation of f . Let 0 < δ < 1. Define Fδ = {f : f continuous and for some C > 0 and for all n ∈ N, varnf ™ Cδn}.