Birational transformations preserving rational solutions of algebraic ordinary differential equations

• L.X.C. Ngô ^[1] ; J.R. Sendra ^[2] ; F. Winkler ^[3]
  1. [1] Quy Nhon University

     Quy Nhon University

     Vietnam

     
  2. [2] Universidad de Alcalá

     Universidad de Alcalá

     Alcalá de Henares, España

     
  3. [3] Johannes Kepler University of Linz

     Johannes Kepler University of Linz

     Linz, Austria

     

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 286, Nº 1 (1 October 2015), 2015, págs. 114-127
• Idioma: inglés
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• Resumen

  • We characterize the set of all rational transformations with the property of preserving the existence of rational solutions of algebraic ordinary differential 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.