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

  1. Cano Torres, José María 1
  2. Fortuny Ayuso, Pedro 2
  3. Ribón, Javier 3
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

  2. 2 Universidad de Oviedo
    info

    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

  3. 3 Universidade Federal Fluminense (Brasil)
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Journal:
Publicacions matematiques

ISSN: 0214-1493

Year of publication: 2024

Volume: 68

Issue: 2

Pages: 331-358

Type: Article

DOI: 10.5565/PUBLMAT6822401 DIALNET GOOGLE SCHOLAR lock_openDDD editor

More publications in: Publicacions matematiques

Abstract

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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