Birational transformations preserving rational solutions of algebraic ordinary differential equations

Authors
Ngo, L.X.Chau; Sendra Pons, Juan RafaelUniversity of Alcalá Author; Winkler, FranzUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/28564
DOI: 10.1016/j.cam.2015.03.007
ISSN: 0377-0427
Publisher
Elsevier
Date
2015-05-01
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Economía y Competitividad
Austrian Science Fund (FWF)
Bibliographic citation
Journal of Computational and Applied Mathematics, 2015, v. 286, p. 114-127
Keywords
Rational parametrization
Integral curve
Integral birational transformation
Rational solution
Algebraic diferential equation
Description / Notes
J.R. Sendra belongs to the Research Group ASYNACS
Project
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
W1214-N15, project DK11 (Austrian Science Fund (FWF))
Document type
info:eu-repo/semantics/preprint
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
http://dx.doi.org/10.1016/j.cam.2015.03.007
Rights
© Elsevier B.V., 2015
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We characterize the set of all rational transformations with the property of pre- serving the existence of rational solutions of algebraic ordinary di erential equations (AODEs). This set is a group under composition and, by its action, partitions the set of AODEs into equivalence classes for which the existence of rational solutions is an invariant property. Moreover, we describe how the rational solutions, if any, of two different AODEs in the same class are related.
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