An asymptotic analysis in thermodynamic formalism

摘要

We consider an asymptotic behaviour of the topological pressure, the Gibbs measure and the measure-theoretic entropy concerning a potential defined on a subshift. Our results are obtained by considering asymptotic perturbation of transfer operators and by using a method that avoids resolvent’s perturbation. In application, we investigate an asymptotic behaviour of the Hausdorff dimension of a perturbed cookie-cutter set.