Description

• Title:
  Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space
• Creator:
  Sabatini, Marco
• Description:
  Fessler and Gutierrez \cite{Fe}, \cite{Gu} proved that if a non-singular planar map has Jacobian matrix without eigenvalues in $(0,+\infty)$, then it is injective. We prove that the same holds replacing $(0,+\infty)$ with any unbounded curve disconnecting the upper (lower) complex half-plane. Additionally we prove that a Jacobian map $(P,Q)$ is injective if $\partial P/\partial x + \partial Q/\partial y$ is not a surjective function.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Marco Sabatini
• Date:
  2023.09.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 62, No 1 (September 2023); 367 - 375;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/46316/36569 ;https://apcz.umk.pl/TMNA/article/view/46316/36570
• Subject:
  Jacobian conjecture;
  global injectivity;
  eigenvalue continuity;
  Primary: 14R15;
  Secondary: 26B10
• Identifier: https://apcz.umk.pl/TMNA/article/view/46316
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other