dc.contributor.author | Cano, José | |
dc.contributor.author | Falkensteiner, Sebastian | |
dc.contributor.author | Robertz, Daniel | |
dc.contributor.author | Sendra Pons, Juan Rafael | |
dc.date.accessioned | 2022-05-03T14:20:21Z | |
dc.date.available | 2022-05-03T14:20:21Z | |
dc.date.issued | 2022-04-22 | |
dc.identifier.bibliographicCitation | Cano, J., Falkensteiner, S., Robertz, D. & Sendra, J.R. 2023, "Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables", Journal of Symbolic Computation, vol. 114, pp. 1-17. | |
dc.identifier.issn | 0747-7171 | |
dc.identifier.uri | http://hdl.handle.net/10017/51628 | |
dc.description.abstract | In this paper we study systems of autonomous algebraic ODEs
in several differential indeterminates. We develop a notion of
algebraic dimension of such systems by considering them as
algebraic systems. Afterwards we apply differential elimination
and analyze the behavior of the dimension in the resulting
Thomas decomposition. For such systems of algebraic dimension
one, we show that all formal Puiseux series solutions can be
approximated up to an arbitrary order by convergent solutions. We
show that the existence of Puiseux series and algebraic solutions
can be decided algorithmically. Moreover, we present a symbolic
algorithm to compute all algebraic solutions. The output can
either be represented by triangular systems or by their minimal
polynomials. | en |
dc.description.sponsorship | Agencia Estatal de Investigación | es_ES |
dc.description.sponsorship | Austrian Science Fund | en |
dc.format.mimetype | application/pdf | en |
dc.language.iso | eng | en |
dc.publisher | Elsevier | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Algebraic autonomous ordinary differential equation | en |
dc.subject | Puiseux series solution | en |
dc.subject | Convergent solution | en |
dc.subject | Artin approximation | en |
dc.subject | Algebraic solution | en |
dc.subject | Thomas decomposition | en |
dc.title | Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables | en |
dc.type | info:eu-repo/semantics/article | en |
dc.subject.eciencia | Matemáticas | es_ES |
dc.subject.eciencia | Mathematics | en |
dc.contributor.affiliation | Universidad de Alcalá. Departamento de Física y Matemáticas: Unidad docente Matemáticas | es_ES |
dc.date.updated | 2022-05-03T14:19:31Z | |
dc.relation.publisherversion | https://doi.org/10.1016/j.jsc.2022.04.012 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | en |
dc.identifier.doi | 10.1016/j.jsc.2022.04.012 | |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105621GB-I00/ES/METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOS/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113192GB-I00/ES/VISUALIZACION MATEMATICA: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/ | es_ES |
dc.relation.projectID | P 31327-N32 (Austrian Science Fund) | en |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | en |
dc.identifier.uxxi | AR/0000041088 | |
dc.identifier.publicationtitle | Journal of Symbolic Computation | |
dc.identifier.publicationvolume | 114 | |
dc.identifier.publicationlastpage | 17 | |
dc.identifier.publicationfirstpage | 1 | |