Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem
Resumen:
We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x,dxu)=h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marchal’s Theorem, whose main use in recent literature has been to prove the existence of periodic orbits.
| 2020 | |
| MATH AmSud Sidiham, CSIC grupo 618 e IFUM LIA-CNRS. | |
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N-body problem Hamilton-Jacobi equation Viscosity solutions |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
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https://annals.math.princeton.edu/2020/192-2/p05
https://hdl.handle.net/20.500.12008/36121 |
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| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522889963929600 |
|---|---|
| author | Maderna, Ezequiel |
| author2 | Venturelli, Andrea |
| author2_role | author |
| author_facet | Maderna, Ezequiel Venturelli, Andrea |
| author_role | author |
| bitstream.checksum.fl_str_mv | 6429389a7df7277b72b7924fdc7d47a9 a006180e3f5b2ad0b88185d14284c0e0 8c146f9755c137d266000df56aae59c9 1996b8461bc290aef6a27d78c67b6b52 b8a29ba04519f39971b3ea967a79e405 |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 MD5 MD5 MD5 |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Maderna Ezequiel, Universidad de la República (Uruguay). Facultad de Ingeniería. Venturelli Andrea, Laboratoire de Mathématiques d'Avignon, Avignon, France |
| dc.creator.none.fl_str_mv | Maderna, Ezequiel Venturelli, Andrea |
| dc.date.accessioned.none.fl_str_mv | 2023-03-03T12:55:38Z |
| dc.date.available.none.fl_str_mv | 2023-03-03T12:55:38Z |
| dc.date.issued.none.fl_str_mv | 2020 |
| dc.description.abstract.none.fl_txt_mv | We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x,dxu)=h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marchal’s Theorem, whose main use in recent literature has been to prove the existence of periodic orbits. |
| dc.description.sponsorship.none.fl_txt_mv | MATH AmSud Sidiham, CSIC grupo 618 e IFUM LIA-CNRS. |
| dc.format.extent.es.fl_str_mv | 51 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Maderna, E. y Venturelli, A. "Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem". Annals of Mathematics. [en línea]. 2020, vol. 192, no. 2, pp. 499-550. DOI: 10.4007/annals.2020.192.2.5. |
| dc.identifier.doi.none.fl_str_mv | 10.4007/annals.2020.192.2.5 |
| dc.identifier.issn.none.fl_str_mv | 0003-486X |
| dc.identifier.uri.none.fl_str_mv | https://annals.math.princeton.edu/2020/192-2/p05 https://hdl.handle.net/20.500.12008/36121 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | Princeton University |
| dc.relation.ispartof.es.fl_str_mv | Annals of Mathematics, vol. 192, no. 2, 2020, pp. 499-550. |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-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 | N-body problem Hamilton-Jacobi equation Viscosity solutions |
| dc.title.none.fl_str_mv | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem |
| 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 | We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x,dxu)=h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marchal’s Theorem, whose main use in recent literature has been to prove the existence of periodic orbits. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_80a69c477f56d7170f1a11c0070440b3 |
| identifier_str_mv | Maderna, E. y Venturelli, A. "Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem". Annals of Mathematics. [en línea]. 2020, vol. 192, no. 2, pp. 499-550. DOI: 10.4007/annals.2020.192.2.5. 0003-486X 10.4007/annals.2020.192.2.5 |
| 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:20.500.12008/36121 |
| publishDate | 2020 |
| 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 - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Maderna Ezequiel, Universidad de la República (Uruguay). Facultad de Ingeniería.Venturelli Andrea, Laboratoire de Mathématiques d'Avignon, Avignon, France2023-03-03T12:55:38Z2023-03-03T12:55:38Z2020Maderna, E. y Venturelli, A. "Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem". Annals of Mathematics. [en línea]. 2020, vol. 192, no. 2, pp. 499-550. DOI: 10.4007/annals.2020.192.2.5.0003-486Xhttps://annals.math.princeton.edu/2020/192-2/p05https://hdl.handle.net/20.500.12008/3612110.4007/annals.2020.192.2.5We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x,dxu)=h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marchal’s Theorem, whose main use in recent literature has been to prove the existence of periodic orbits.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2023-03-02T01:41:11Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) MV20.pdf: 737544 bytes, checksum: b8a29ba04519f39971b3ea967a79e405 (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2023-03-02T18:51:30Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) MV20.pdf: 737544 bytes, checksum: b8a29ba04519f39971b3ea967a79e405 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-03-03T12:55:38Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) MV20.pdf: 737544 bytes, checksum: b8a29ba04519f39971b3ea967a79e405 (MD5) Previous issue date: 2020MATH AmSud Sidiham, CSIC grupo 618 e IFUM LIA-CNRS.51 p.application/pdfenengPrinceton UniversityAnnals of Mathematics, vol. 192, no. 2, 2020, pp. 499-550.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 - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)N-body problemHamilton-Jacobi equationViscosity solutionsViscosity solutions and hyperbolic motions : a new PDE method for the N-body problemArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaMaderna, EzequielVenturelli, AndreaLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/36121/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/36121/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem Maderna, Ezequiel N-body problem Hamilton-Jacobi equation Viscosity solutions |
| status_str | publishedVersion |
| title | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem |
| title_full | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem |
| title_fullStr | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem |
| title_full_unstemmed | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem |
| title_short | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem |
| title_sort | Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem |
| topic | N-body problem Hamilton-Jacobi equation Viscosity solutions |
| url | https://annals.math.princeton.edu/2020/192-2/p05 https://hdl.handle.net/20.500.12008/36121 |
