Asymptotic solution of Bowen equation for perturbed potentials on shift spaces with countable states.

In this paper, we study the asymptotic expansions for the zero of the pressure function s ↦ P(sφ(ε, ⋅)+ξ(ε, ⋅)) for perturbed potentials φ(ε, ⋅) and ξ(ε, ⋅) defined on the shift space with countable state space. In our main result, we give a sufficient condition for the solution s = s(ε) of P(sφ(ε, ⋅) + ξ(ε, ⋅)) = 0 to have the n-order asymptotic expansion for the small parameter ε. In addition, we also obtain the case where the order of the expansion of the solution s = s(ε) is less than the order of the expansion of the perturbed potentials. Our results can be applied to problems concerning asymptotic behaviours of Hausdorff dimensions given by the Bowen formula: conformal graph directed Markov systems and other concrete examples. [ABSTRACT FROM AUTHOR]