Rescaled expansive measures for flows
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915457403977728 |
|---|---|
| author | Yang, Yun |
| author_facet | Yang, Yun |
| contents | We introduce the notion of rescaled expansive measures to study a measure-theoretic formulation of rescaled expansiveness for flows, particularly in the presence of singularities. Equivalent definitions are established via reparametrizations of different regularities. Under the assumption of positive entropy, we prove the existence of invariant rescaled expansive measures. In the appendix, we derive a rescaled version of the Brin-Katok local entropy formula for flows, extending [7] from nonsingular flows to general flows that may include singularities. This framework provides new tools for understanding entropy and expansiveness in continuous-time dynamical systems with singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rescaled expansive measures for flows Yang, Yun Dynamical Systems 37A35, 37C10, 37C40 We introduce the notion of rescaled expansive measures to study a measure-theoretic formulation of rescaled expansiveness for flows, particularly in the presence of singularities. Equivalent definitions are established via reparametrizations of different regularities. Under the assumption of positive entropy, we prove the existence of invariant rescaled expansive measures. In the appendix, we derive a rescaled version of the Brin-Katok local entropy formula for flows, extending [7] from nonsingular flows to general flows that may include singularities. This framework provides new tools for understanding entropy and expansiveness in continuous-time dynamical systems with singularities. |
| title | Rescaled expansive measures for flows |
| topic | Dynamical Systems 37A35, 37C10, 37C40 |
| url | https://arxiv.org/abs/2508.16536 |