An application of a nonuniform global stability problem to the study of parametrized polynomial automorphisms
Algebraic Geometry
2025-01-22 v8
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.
Keywords
Cite
@article{arxiv.2108.06416,
title = {An application of a nonuniform global stability problem to the study of parametrized polynomial automorphisms},
author = {Álvaro Castañeda and Ignacio Huerta and Gonzalo Robledo},
journal= {arXiv preprint arXiv:2108.06416},
year = {2025}
}