Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
Identificadores
Enlace permanente (URI): http://hdl.handle.net/10017/51628DOI: 10.1016/j.jsc.2022.04.012
ISSN: 0747-7171
Editor
Elsevier
Fecha de publicación
2022-04-22Patrocinadores
Agencia Estatal de Investigación
Austrian Science Fund
Cita bibliográfica
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.
Palabras clave
Algebraic autonomous ordinary differential equation
Puiseux series solution
Convergent solution
Artin approximation
Algebraic solution
Thomas decomposition
Proyectos
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/
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/
P 31327-N32 (Austrian Science Fund)
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/publishedVersion
Versión del editor
https://doi.org/10.1016/j.jsc.2022.04.012Derechos
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
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.
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Colecciones
- MATEMATIC - Artículos [172]