Abstract
In this note we revisit a result of Sabatini relating global injectivity of polynomial maps to global centers in the plane. We deliver a generalization of this result for \(C^2\) maps defined on connected sets. The shape of the image is taking into account. Here we do not use Hadamard’s invertibility theorem.
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Acknowledgements
We thank the reviewers for the helpful comments and suggestions that improved the presentation of the paper. The first named author was partially supported by a BPE-FAPESP Grant Number 2014/ 26149-3. The second named author was partially supported by a MINECO Grant Number MTM2013-40998-P, an AGAUR Grant Number 2014SGR 568 and two FP7-PEOPLE-2012-IRSES Grants Numbers 316338 and 318999. Both authors were also partially supported by a CAPES CSF–PVE Grant 88881.030454/ 2013-01 from the program CSF-PVE.
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Braun, F., Llibre, J. On the Connection Between Global Centers and Global Injectivity in the Plane. Differ Equ Dyn Syst (2023). https://doi.org/10.1007/s12591-023-00630-5
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DOI: https://doi.org/10.1007/s12591-023-00630-5