Reciprocal Transformations and Their Discrete Maharam Extensions
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913919711313920 |
|---|---|
| author | Johnson, Chris |
| author_facet | Johnson, Chris |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reciprocal Transformations and Their Discrete Maharam Extensions Johnson, Chris Dynamical Systems 37A40 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. |
| title | Reciprocal Transformations and Their Discrete Maharam Extensions |
| topic | Dynamical Systems 37A40 |
| url | https://arxiv.org/abs/2501.00408 |