Natural extensions for piecewise affine maps via Hofbauer towers

TL;DR

This paper introduces a method using Hofbauer towers to explicitly construct natural extensions of measure-preserving endomorphisms, with applications to specific examples in dynamical systems.

Contribution

It provides a novel explicit construction technique for natural extensions of piecewise affine maps using Hofbauer towers.

Findings

Explicit construction of natural extensions for certain maps

Applications to specific dynamical systems examples

Enhanced understanding of measure-preserving endomorphisms

Abstract

We use canonical Markov extensions (Hofbauer towers) to give an explicit construction of the natural extensions of various measure preserving endomorphisms, and present some applications to particular examples.