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arXiv · 2108.06416

An application of a nonuniform global stability problem to the study of parametrized polynomial automorphisms

Álvaro Castañeda·Ignacio Huerta·Gonzalo Robledo
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Abstract

We propose a handful of definitions of injectivity for a parametrized family of maps and study its link with a global nonuniform stability conjecture for nonautonomous differential systems, which has been recently introduced. This relation allow us to address a particular family of parametrized polynomial automorphisms and to prove that they have polynomial inverse for certain parameters, which is reminiscent to the Jacobian Conjecture.

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Álvaro Castañeda, Ignacio Huerta, Gonzalo Robledo. 2021-08-13. An application of a nonuniform global stability problem to the study of parametrized polynomial automorphisms. https://arxiv.org/abs/2108.06416

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