Central Limit Theorem for Sequential Dynamical Systems

TL;DR

This paper develops a new method using projective metrics on complex cones to prove the Central Limit Theorem with error bounds for sequential dynamical systems, including new results for sequential dispersing billiards.

Contribution

It introduces a novel approach applying projective metrics to establish CLT with error bounds for a broad class of sequential dynamical systems, including previously unstudied billiards.

Findings

Established CLT with error bounds for sequential expanding maps.

Extended CLT results to sequential dispersing billiards.

Demonstrated the effectiveness of the projective metric approach.

Abstract

We present a general approach to establish the Central Limit Theorem with error bounds for sequential dynamical systems. The main tool we develop is the application to this setting of a projective metric on complex cones, following the ideas introduced by Rugh and Dubois. To demonstrate the power of the proposed setting, we apply it to both sequential expanding maps, where similar results are known, and to sequential dispersing billiards, for which no such results are currently known.