Complexity of Puiseux solutions of differential and q -difference equations of order and degree one

• Cano Torres, José María ^[1] ; Fortuny Ayuso, Pedro ^[2] ; Ribón, Javier ^[3]
  1. [1] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     
  2. [2] Universidad de Oviedo

     Universidad de Oviedo

     Oviedo, España

     
  3. [3] Universidade Federal Fluminense

     Universidade Federal Fluminense

     Brasil

     

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• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 2, 2024, págs. 331-358
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6822401
• Enlaces
  • Texto completo
• Resumen

  • We relate the complexity of both differential and q-difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are complicated, theinitial equation is complicated too. In this spirit, we bound from below an invariant of the differential or q-difference equation, the height of its Newton polygon, in terms of the characteristic factors of a solution. The differential and the q-difference cases are treated in a unified way.

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