Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature
For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to a class of torus extensions of Anosov flows, subject to assu...
Saved in:
| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
03.08.2025
|
| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2508.01593 |
Cover
| Abstract | For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to a class of torus extensions of Anosov flows, subject to assumptions on the Brin transitivity group and the smoothness of the stable subbundle. Our approach is based on a simplified dynamical model for studying the extension flow, constructed via a Young tower of the underlying Anosov flow. Exponential mixing is then obtained through a strengthened Dolgopyat type estimate on the corresponding transfer operators. |
|---|---|
| AbstractList | For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to a class of torus extensions of Anosov flows, subject to assumptions on the Brin transitivity group and the smoothness of the stable subbundle. Our approach is based on a simplified dynamical model for studying the extension flow, constructed via a Young tower of the underlying Anosov flow. Exponential mixing is then obtained through a strengthened Dolgopyat type estimate on the corresponding transfer operators. |
| Author | Zhang, Daofei Pollicott, Mark |
| Author_xml | – sequence: 1 givenname: Mark surname: Pollicott fullname: Pollicott, Mark – sequence: 2 givenname: Daofei surname: Zhang fullname: Zhang, Daofei |
| BackLink | https://doi.org/10.48550/arXiv.2508.01593$$DView paper in arXiv |
| BookMark | eNqFzj0OgkAQQOEttPDvAFbOBURQSbQ2Gg9gTyYwC5PALA4L4u0VYm_1mq94czMRJ2TMOgqD4ymOwx1qz12wj8NTEEbx-TAz-bWvv0g8YwkV9yw5OAtWsSKwpXs1YJ2CL5QIMq5IGnYyWBS2rsyagT9bVE-6rVnSgjIQytFzR5C22qFvlZZmarFsaPXrwmxu18flvh2Xklq5Qn0nw1oyrh3-iw-PfEge |
| ContentType | Journal Article |
| Copyright | http://creativecommons.org/publicdomain/zero/1.0 |
| Copyright_xml | – notice: http://creativecommons.org/publicdomain/zero/1.0 |
| DBID | GOX |
| DOI | 10.48550/arxiv.2508.01593 |
| DatabaseName | arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 2508_01593 |
| GroupedDBID | GOX |
| ID | FETCH-arxiv_primary_2508_015933 |
| IEDL.DBID | GOX |
| IngestDate | Thu Aug 07 11:51:10 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-arxiv_primary_2508_015933 |
| OpenAccessLink | https://arxiv.org/abs/2508.01593 |
| ParticipantIDs | arxiv_primary_2508_01593 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-08-03 |
| PublicationDateYYYYMMDD | 2025-08-03 |
| PublicationDate_xml | – month: 08 year: 2025 text: 2025-08-03 day: 03 |
| PublicationDecade | 2020 |
| PublicationYear | 2025 |
| Score | 3.8385267 |
| SecondaryResourceType | preprint |
| Snippet | For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Dynamical Systems |
| Title | Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature |
| URI | https://arxiv.org/abs/2508.01593 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV07T8MwED61nVgQCFB538BqsJKQpCNCLRUSsICULYpfpVJJSh6Qn4_PLoKlq-9knezh--7hzwBXMimIh3Im01CwSMaGpcZEjHPFBZ8oXQgq6D89x_O36DG7zQaAv29hirpffnl9YNHcWHxOry1gTcIhDIOAkquHl8w3J50U18b_z89yTLf0DyRme7C7YXd4569jHwa6PIDFtF9XJU3lWNPHsrdggZVBQ2NRaFbVd4OWOWJrT1WjIrV9r5SBJE1hqpVqyP3TT18yklN41wpLvXCa3Sg7Kqt2tT6Ey9n09X7OXGj52utI5BR17qIOj2Bks309BpTKYrYMCp4KmxkZVchEqrTQSlKPOE6OYbxtl5PtplPYCejjWpp1CM9g1NadPrdo2ooLd6Q_Top83w |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Exponential+mixing+of+frame+flows+for+three+dimensional+manifolds+of+quarter-pinched+negative+curvature&rft.au=Pollicott%2C+Mark&rft.au=Zhang%2C+Daofei&rft.date=2025-08-03&rft_id=info:doi/10.48550%2Farxiv.2508.01593&rft.externalDocID=2508_01593 |