A new class of non-injective polynomial local diffeomorphisms on the\n plane

2020/03/23 by Filipe Fernandes, Fernandes, Filipe
Engineering · Mathematics · Physics and Astronomy · #14R15 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Control and Dynamics of Mobile Robots #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2003.10226

openalex publication_date 2020/03/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this short note we provide the example with the lowest degree known so far\nof a non-injective local polynomial diffeomorphism F=(p,q):\ℝ² \→\n\ℝ². In our example p has degree 10 and q has degree 15,\nrather than 10 and 25, respectively, known up to now as the smallest\ndegrees for the coordinates of F. Our construction was based on S. Pinchuk\ncelebrated counterexample to the real Jacobian conjecture.\n

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