Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space
Classical Analysis and ODEs
2022-02-14 v1
Abstract
Fessler and Gutierrez \cite{Fe,Gu} proved that if a non-singular planar map has Jacobian matrix without eigenvalues in , then it is injective. We prove that the same holds replacing with any unbounded curve disconnecting the upper (lower) complex half-plane. Additionally we prove that a Jacobian map is injective if is not a surjective function.
Cite
@article{arxiv.2202.05542,
title = {Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space},
author = {Marco Sabatini},
journal= {arXiv preprint arXiv:2202.05542},
year = {2022}
}