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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

  • Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 286, Nº 1 (1 October 2015), 2015, págs. 114-127
  • Idioma: inglés
  • DOI: 10.1016/j.cam.2015.03.007
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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.


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