Flow techniques for non-geometric RDEs on manifolds
In 2015, Bailleul presented a mechanism to solve rough differential equations by constructing flows, using the log-ODE method. We extend this notion in two ways: On the one hand, we localize Bailleul's notion of an almost-flow to solve RDEs on manifolds. On the other hand, we extend his results...
| Main Authors: | , |
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| Format: | Internet publication |
| Language: | English |
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2023
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| _version_ | 1826312206008975360 |
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| author | Kern, H Lyons, T |
| author_facet | Kern, H Lyons, T |
| author_sort | Kern, H |
| collection | OXFORD |
| description | In 2015, Bailleul presented a mechanism to solve rough differential equations by constructing flows, using the log-ODE method. We extend this notion in two ways: On the one hand, we localize Bailleul's notion of an almost-flow to solve RDEs on manifolds. On the other hand, we extend his results to non-geometric rough paths, living in any connected, cocommutative, graded Hopf algebra. This requires a new concept, which we call a pseudo bialgebra map. We further connect our results to Curry et al (2020), who solved planarly branched RDEs on homogeneous spaces. |
| first_indexed | 2024-03-07T08:24:03Z |
| format | Internet publication |
| id | oxford-uuid:064151c3-c999-460f-8463-e235f74b6a62 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:24:03Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | oxford-uuid:064151c3-c999-460f-8463-e235f74b6a622024-02-12T16:28:36ZFlow techniques for non-geometric RDEs on manifoldsInternet publicationhttp://purl.org/coar/resource_type/c_7ad9uuid:064151c3-c999-460f-8463-e235f74b6a62EnglishSymplectic Elements2023Kern, HLyons, TIn 2015, Bailleul presented a mechanism to solve rough differential equations by constructing flows, using the log-ODE method. We extend this notion in two ways: On the one hand, we localize Bailleul's notion of an almost-flow to solve RDEs on manifolds. On the other hand, we extend his results to non-geometric rough paths, living in any connected, cocommutative, graded Hopf algebra. This requires a new concept, which we call a pseudo bialgebra map. We further connect our results to Curry et al (2020), who solved planarly branched RDEs on homogeneous spaces. |
| spellingShingle | Kern, H Lyons, T Flow techniques for non-geometric RDEs on manifolds |
| title | Flow techniques for non-geometric RDEs on manifolds |
| title_full | Flow techniques for non-geometric RDEs on manifolds |
| title_fullStr | Flow techniques for non-geometric RDEs on manifolds |
| title_full_unstemmed | Flow techniques for non-geometric RDEs on manifolds |
| title_short | Flow techniques for non-geometric RDEs on manifolds |
| title_sort | flow techniques for non geometric rdes on manifolds |
| work_keys_str_mv | AT kernh flowtechniquesfornongeometricrdesonmanifolds AT lyonst flowtechniquesfornongeometricrdesonmanifolds |