On the connection between global centers and global injectivity in the plane

TL;DR

This paper generalizes a known relation between global injectivity and centers in planar systems, considering the shape of the image, and provides proofs without relying on Hadamard's theorem.

Contribution

It introduces a broader connection between global centers and injectivity, extending previous results by Sabatini without using Hadamard's theorem.

Findings

Established a generalized relation between global centers and injectivity

Provided proofs that do not depend on Hadamard's theorem

Enhanced understanding of the image shape in planar maps

Abstract

In this note we present a generalization of a result of Sabatini relating global injectivity and global centers. The shape of the image of the map is taking into account. Our proofs do not use Hadamard's theorem.