Asymptotic solution of Bowen equation for perturbed potentials defined on shift spaces (Research on the Theory of Random Dynamical Systems and Fractal Geometry)

Abstract

We study the asymptotic solution of the equation of the pressure function s→ P（sΦε） for a perturbed potential Φε defined on a shift space with countable state. We show that if the perturbed potential Φε has an asymptotic expansion for a small parameter c and some conditions are satisfied, then the solution s = s(ε) of P(sΦε) ＝ 0 has also an asymptotic behaviour with same order. In addition, we also give the case where the order of the expansion of the solutions= s(ε) is less than the order of the expansion of the perturbed potential Φε. Ourresults can be applied to problems concerning asymptotic behaviors of Hausdorff dimensions obtained from Bowen formula.