Convergence of the Ruelle operator for a function satisfying Bowen’s condition

By P. Walters. 2000

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KMS states on C^*-algebras associated to expansive maps (2003, background): “Definition 2.7. (see [ W3 , §1], [Ru]) A function ϕ ∈ C(X;R) is said to satisfy the Bowen condition with respect to T : X → X if there are δ, C > 0 such that”
On Khintchine exponents and Lyapunov exponents of continued fractions (2008, unknown): “Furthermore the dimension function t̃(ξ) has the following properties: 1) t̃(λ0) = 1 and t̃(+∞) = 1/2; 2) t̃′(β) < 0 for all β > λ0, t̃′(λ0) = 0, and t̃′(β) > 0 for all β < λ0; 3) t̃′(γ0+) = +∞ and t̃′(+∞) = 0;”