A generalized Grobman–Hartman theorem for nonautonomous dynamics

• Backes, Lucas ^[1] ; Dragičević, Davor ^[2]
  1. [1] Universidade Federal do Rio Grande do Sul

     Universidade Federal do Rio Grande do Sul

     Brasil

     
  2. [2] University of Rijeka

     University of Rijeka

     Croacia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 3, 2022, págs. 411-431
• Idioma: inglés
• DOI: 10.1007/s13348-021-00327-4
• Texto completo no disponible (Saber más ...)
• Resumen

  • The purpose of this note is to extend the recent generalized version of the Grobman–Hartman theorem established by Bernardes Jr. and Messaoudi from an autonomous to nonautonomous dynamics. More precisely, we prove that any sufficiently small perturbation of a nonautonomous linear dynamics that admits a generalized exponential dichotomy is topologically conjugated to its linear part. In addition, we prove that under certain mild additional conditions, the conjugacy is in fact Hölder continuous.