Singularities for analytic continuations of holonomy germs of riccati foliations
Resumen:
In this paper we study the problem of analytic extension of holonomy germs of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all the holonomy germs between a fiber and the corresponding holomorphic section of the bundle are led to singularities by almost every developed geodesic ray. We study in detail the distribution of these singularities and prove in particular that they form a dense uncountable subset of the limit set. This gives another negative answer to a conjecture of Loray using a completely different method, namely the ergodic study of the foliated geodesic flow.
| 2016 | |
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Analytic continuation Foliated geodesic flow Lyapunov exponents Riccati foliation |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/22561 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0) |
| _version_ | 1807522781864132608 |
|---|---|
| author | Álvarez, Sebastien |
| author2 | Hussenot, N. |
| author2_role | author |
| author_facet | Álvarez, Sebastien Hussenot, N. |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Alvarez Sebastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática Hussenot N. |
| dc.creator.none.fl_str_mv | Álvarez, Sebastien Hussenot, N. |
| dc.date.accessioned.none.fl_str_mv | 2019-11-27T17:47:43Z |
| dc.date.available.none.fl_str_mv | 2019-11-27T17:47:43Z |
| dc.date.issued.none.fl_str_mv | 2016 |
| dc.description.abstract.none.fl_txt_mv | In this paper we study the problem of analytic extension of holonomy germs of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all the holonomy germs between a fiber and the corresponding holomorphic section of the bundle are led to singularities by almost every developed geodesic ray. We study in detail the distribution of these singularities and prove in particular that they form a dense uncountable subset of the limit set. This gives another negative answer to a conjecture of Loray using a completely different method, namely the ergodic study of the foliated geodesic flow. |
| dc.format.extent.es.fl_str_mv | 46 h |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Álvarez, S., Hussenot, N. "Singularities for analytic continuations of holonomy germs of riccati foliations". Annales de l'Institut Fourier [en línea]. 2016, 66 (1), 331-376. doi: 10.5802/aif.3013 |
| dc.identifier.doi.none.fl_str_mv | 10.5802/aif.3013 |
| dc.identifier.issn.none.fl_str_mv | 0373-0956 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/22561 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | Association des Annales de l'Institut Fourier |
| dc.relation.ispartof.es.fl_str_mv | Annales de l'Institut Fourier, 2016, 66 (1), 331-376. |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Analytic continuation Foliated geodesic flow Lyapunov exponents Riccati foliation |
| dc.title.none.fl_str_mv | Singularities for analytic continuations of holonomy germs of riccati foliations |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | In this paper we study the problem of analytic extension of holonomy germs of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all the holonomy germs between a fiber and the corresponding holomorphic section of the bundle are led to singularities by almost every developed geodesic ray. We study in detail the distribution of these singularities and prove in particular that they form a dense uncountable subset of the limit set. This gives another negative answer to a conjecture of Loray using a completely different method, namely the ergodic study of the foliated geodesic flow. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_94a9a3863a08d068549cc95d9b9e7dda |
| identifier_str_mv | Álvarez, S., Hussenot, N. "Singularities for analytic continuations of holonomy germs of riccati foliations". Annales de l'Institut Fourier [en línea]. 2016, 66 (1), 331-376. doi: 10.5802/aif.3013 0373-0956 10.5802/aif.3013 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/22561 |
| publishDate | 2016 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0) |
| spelling | Alvarez Sebastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de MatemáticaHussenot N.2019-11-27T17:47:43Z2019-11-27T17:47:43Z2016Álvarez, S., Hussenot, N. "Singularities for analytic continuations of holonomy germs of riccati foliations". Annales de l'Institut Fourier [en línea]. 2016, 66 (1), 331-376. doi: 10.5802/aif.30130373-0956https://hdl.handle.net/20.500.12008/2256110.5802/aif.3013In this paper we study the problem of analytic extension of holonomy germs of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all the holonomy germs between a fiber and the corresponding holomorphic section of the bundle are led to singularities by almost every developed geodesic ray. We study in detail the distribution of these singularities and prove in particular that they form a dense uncountable subset of the limit set. This gives another negative answer to a conjecture of Loray using a completely different method, namely the ergodic study of the foliated geodesic flow.Submitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2019-11-27T12:58:36Z No. of bitstreams: 2 license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) 105802aif3013.pdf: 820699 bytes, checksum: abdee065edc183c1d0131d62b38b7da3 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2019-11-27T17:35:16Z (GMT) No. of bitstreams: 2 license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) 105802aif3013.pdf: 820699 bytes, checksum: abdee065edc183c1d0131d62b38b7da3 (MD5)Made available in DSpace on 2019-11-27T17:47:43Z (GMT). No. of bitstreams: 2 license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) 105802aif3013.pdf: 820699 bytes, checksum: abdee065edc183c1d0131d62b38b7da3 (MD5) Previous issue date: 201646 happlication/pdfenengAssociation des Annales de l'Institut FourierAnnales de l'Institut Fourier, 2016, 66 (1), 331-376.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0)Analytic continuationFoliated geodesic flowLyapunov exponentsRiccati foliationSingularities for analytic continuations of holonomy germs of riccati foliationsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaÁlvarez, SebastienHussenot, N.LICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/22561/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-847http://localhost:8080/xmlui/bitstream/20.500.12008/22561/2/license_url2e02f7f19671f565f98e3666cf2e95aeMD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Singularities for analytic continuations of holonomy germs of riccati foliations Álvarez, Sebastien Analytic continuation Foliated geodesic flow Lyapunov exponents Riccati foliation |
| status_str | publishedVersion |
| title | Singularities for analytic continuations of holonomy germs of riccati foliations |
| title_full | Singularities for analytic continuations of holonomy germs of riccati foliations |
| title_fullStr | Singularities for analytic continuations of holonomy germs of riccati foliations |
| title_full_unstemmed | Singularities for analytic continuations of holonomy germs of riccati foliations |
| title_short | Singularities for analytic continuations of holonomy germs of riccati foliations |
| title_sort | Singularities for analytic continuations of holonomy germs of riccati foliations |
| topic | Analytic continuation Foliated geodesic flow Lyapunov exponents Riccati foliation |
| url | https://hdl.handle.net/20.500.12008/22561 |
