Effective equidistribution of periodic orbits for subshifts of finite type

TL;DR

This paper investigates how specific sets of periodic orbits in subshifts of finite type distribute evenly over the space, providing effective results applicable to hyperbolic and expanding maps based on subset growth.

Contribution

It introduces a growth-based approach to establish effective equidistribution for periodic orbits in subshifts of finite type, extending to hyperbolic and expanding dynamical systems.

Findings

Effective equidistribution results derived from subset growth.

Applicable to hyperbolic diffeomorphisms and expanding maps.

Provides quantitative measures of orbit distribution.

Abstract

We study equidistribution of certain subsets of periodic orbits for subshifts of finite type. Our results solely rely on the growth of these subsets. As a consequence, effective equidistribution results are obtained for both hyperbolic diffeomorphisms and expanding maps on compact manifolds.