Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.00408 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We introduce two abstract constructions for building new measurable dynamical systems from existing ones and study their ergodic properties. The first of these constructions, a "reciprocal transformation," produces a type of non-singular transformation where the measures of subsets are distorted in a simple way. We then introduce the "discrete Maharam extension" which associates an infinite measure-preserving transformation to each reciprocal transformations. We give some preliminary results about the ergodic theory of each of these constructions, mention ongoing work, as well as conjectures and questions for future research.