Central Limit Theorems for Non-Invertible Measure Preserving Maps

TL;DR

This paper proves a new functional central limit theorem for non-invertible, possibly non-ergodic measure-preserving maps using the Perron-Frobenius operator, with applications to asymptotically periodic transformations like the tent map.

Contribution

It introduces a novel CLT for a broad class of non-invertible, non-ergodic maps using Perron-Frobenius operators, expanding theoretical understanding.

Findings

Established a new functional CLT for non-invertible maps

Applied the theorem to asymptotically periodic transformations

Provided a detailed example with the tent map

Abstract

We establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic, using the Perron-Frobenius operator. We apply the result to asymptotically periodic transformations and give an extensive specific example of asymptotically periodic transformations by using the tent map.