Stochastic stability of Pollicott–Ruelle resonances
Pollicott-Ruelle resonances for chaotic flows are the characteristic frequencies of correlations. They are typically defined as eigenvalues of the generator of the flow acting on specially designed functional spaces. We show that these resonances can be computed as viscosity limits of eigenvalues of...
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| Format: | Article |
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IOP Publishing
2018
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| Online Access: | http://hdl.handle.net/1721.1/115869 https://orcid.org/0000-0002-6594-7604 |
| _version_ | 1826199099753365504 |
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| author | Zworski, Maciej Dyatlov, Semen |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Zworski, Maciej Dyatlov, Semen |
| author_sort | Zworski, Maciej |
| collection | MIT |
| description | Pollicott-Ruelle resonances for chaotic flows are the characteristic frequencies of correlations. They are typically defined as eigenvalues of the generator of the flow acting on specially designed functional spaces. We show that these resonances can be computed as viscosity limits of eigenvalues of second order elliptic operators. These eigenvalues are the characteristic frequencies of correlations for a stochastically perturbed flow. |
| first_indexed | 2024-09-23T11:14:42Z |
| format | Article |
| id | mit-1721.1/115869 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:14:42Z |
| publishDate | 2018 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1158692022-10-01T02:19:50Z Stochastic stability of Pollicott–Ruelle resonances Zworski, Maciej Dyatlov, Semen Massachusetts Institute of Technology. Department of Mathematics Dyatlov, Semen Pollicott-Ruelle resonances for chaotic flows are the characteristic frequencies of correlations. They are typically defined as eigenvalues of the generator of the flow acting on specially designed functional spaces. We show that these resonances can be computed as viscosity limits of eigenvalues of second order elliptic operators. These eigenvalues are the characteristic frequencies of correlations for a stochastically perturbed flow. 2018-05-24T19:08:39Z 2018-05-24T19:08:39Z 2015-09 2015-07 2018-05-18T17:27:16Z Article http://purl.org/eprint/type/JournalArticle 0951-7715 1361-6544 http://hdl.handle.net/1721.1/115869 Dyatlov, Semyon and Maciej Zworski. “Stochastic Stability of Pollicott–Ruelle Resonances.” Nonlinearity 28, 10 (September 2015): 3511–3533 © 2015 IOP Publishing Ltd & London Mathematical Society https://orcid.org/0000-0002-6594-7604 http://dx.doi.org/10.1088/0951-7715/28/10/3511 Nonlinearity Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IOP Publishing arXiv |
| spellingShingle | Zworski, Maciej Dyatlov, Semen Stochastic stability of Pollicott–Ruelle resonances |
| title | Stochastic stability of Pollicott–Ruelle resonances |
| title_full | Stochastic stability of Pollicott–Ruelle resonances |
| title_fullStr | Stochastic stability of Pollicott–Ruelle resonances |
| title_full_unstemmed | Stochastic stability of Pollicott–Ruelle resonances |
| title_short | Stochastic stability of Pollicott–Ruelle resonances |
| title_sort | stochastic stability of pollicott ruelle resonances |
| url | http://hdl.handle.net/1721.1/115869 https://orcid.org/0000-0002-6594-7604 |
| work_keys_str_mv | AT zworskimaciej stochasticstabilityofpollicottruelleresonances AT dyatlovsemen stochasticstabilityofpollicottruelleresonances |