Description

• Title:
  Normal forms of parabolic logarithmic transseries
• Creator:
  Peran, Dino
• Description:
  We give formal normal forms for parabolic logarithmic transseries $f=z+\dots $, with respect to parabolic logarithmic normalizations. Normalizations are given algorithmically, using fixed point theorems, as limits of Picard's sequences in appropriate complete metric spaces, in contrast to transfinite \emph{term-by-term} eliminations described in former works. Furthermore, we give the explicit formula for the residual coefficient in the normal form and show that, in the larger logarithmic class, we can even eliminate the residual term from the normal form.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Dino Peran
• Date:
  2024.06.16
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 63, No 2 (June 2024); 349 - 412;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/52728/38799 ;https://apcz.umk.pl/TMNA/article/view/52728/38800
• Subject:
  Formal normal forms;
  normalizations;
  logarithmic transseries;
  parabolic fixed point;
  residual invariant;
  fixed point theorems;
  fixed point theory;
  34C20, 37C25, 47H10, 39B12, 46A19, 12J15
• Identifier: https://apcz.umk.pl/TMNA/article/view/52728
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other