Singular perturbation of symbolic dynamics via thermodynamic formalism

Abstract

AbstractWe consider singular perturbation of a mixing subshift of finite type by means of thermodynamic formalism. In our formulation, the perturbed systems are described by a family of potentials {Φ(α,⋅)} with large parameter α on a fixed subshift of finite type, and the original (unperturbed) system is characterized as the system at infinity obtained by collapsing the perturbed system upon taking $\alpha \to \infty $. We apply our formulation to the collapse of cookie-cutter systems and dispersing open billiards.