Polynomial maps with nilpotent Jacobians in dimension three II

2017/10/08 by Dan Yan, Yan, Dan
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Control and Dynamics of Mobile Robots #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1710.02802

openalex publication_date 2017/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, we first classify all polynomial maps of the form H=(u(x,y),v(x,y,z), h(x,y)) in the case that JH is nilpotent and (°_yu,°_yh)≤ 3, H(0)=0. Then we classify all polynomial maps of the form H=(u(x,y,z),v(x,y,u), h(x,y)) in the case that JH is nilpotent and (°v(x,y,0),°h)≤ 3, H(0)=0. Finally, we classify polynomial maps of the form H=(u(x,y,z),v(x,y,z), h(x,y)) in certain conditions.

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