Classification of algebraic ODEs with respect to rational solvability

Authors
Chau Ngo, L. X.; Winkler, FranzUniversity of Alcalá Author; Sendra Pons, Juan RafaelUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20449
DOI: 10.1090/conm/572/11361
ISBN: 9780821868690
Publisher
American Mathematical Society
Date
2012
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Computational Algebraic and Analytic Geometry, 2012, v. 572 p. 193-210
Description / Notes
This is the author’s version of a work that was accepted for publication in Computational Algebraic and Analytic Geometry, AMS series Contemporary Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computational Algebraic and Analytic Geometry vol. 572 pp. 193-210, AMS series Contemporary Mathematics DOI 10.1090/conm/572/11361
Project
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Document type
info:eu-repo/semantics/bookPart
Version
info:eu-repo/semantics/submittedVersion
Publisher's version
http://dx.doi.org/10.1090/conm/572/11361
Rights
© 2012 American Mathematical Society
Access rights
info:eu-repo/semantics/openAccess
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Abstract
In this paper, we introduce a group of affine linear transformations and consider its action on the set of parametrizable algebraic ODEs. In this way the set of parametrizable ODEs is partitioned into classes with an invariant associated system, and hence of equal complexity in terms of rational solvability. We study some special parametrizable ODEs: some well-known and obviously parametrizable classses of ODEs, and some classes of ODEs with special geometric shapes, whose associated systems are characterized by classical ODEs such as separable or homogeneous ones.
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